Some things about comparative linguistics you might just take for granted in your own little corner of a particular language family, until you start looking at how they do things in others. In Uralic studies, we’ve known for 200+ years, and put into explicit practice since 150+ years ago, that progress requires documenting unwritten language varieties (just comparing literary Hungarian / Finnish / Estonian / Sami runs out of steam fast ). For 120+ years, even, that it’s additionally good practice to get detailed interdialectal comparison of such languages started sooner rather than later, not just rely on one well-known doculect.
The big dog of our Eurasian linguistic region, Indo-European studies, has of course an enviable access to a good bunch of attested Old Indians, Old Church Slavonics and Old High Germans, which are lot more directly compareable with each other. But you’d think the field would have somewhere during the 20th century understood at least that, yes, newer-attested languages will have contributions to make to the overall picture too. Remember e.g. how Nuristani, a little bunch of languages up in the mountains of Afghanistan, turned out to have the key evidence for affricate reflexes of *ḱ *ǵʰ *ǵ in Proto-Indo-Iranian, preserved several millennia longer than in Avestan or Sanskrit?
Where Slavistics, Baltistics, Germanistics, Armenistics, Romanistics have all still gotten their general comparative programmes rolling pretty well, Indo-Iranian keeps being a rock that drags behind pretty badly. Considering extra-scientific causes, this is not a giant surprize / is clearly in some amount thanks to these other sub-fields’ status as National Sciences in the various nation-states of Europe. Still, this would not have to be the case, it’s not like Celtistics has been left in the dust. Comparative linguistics also seems like something with sufficiently little direct political valence that it should be doable enough even e.g. under Iran’s current theocratic administration, let alone by the sizable and somewhat intellectual-leaning Iranian diaspora(s). Indian fans of the Out-of-India theory also demonstrate an existing if unorganized interest in linguistic history.
But indeed. Indo-Iranian is not just any random branch of Indo-European; it is today the largest branch (e.g. Glottolog counts 319 varieties, out of 581 Indo-European varieties altogether), and also the only one to preserve all of its known main branches since antiquity. Reflects more branches today than in history, really: already Nuristani is nowhere to be seen until the 19th century. By contrast, in Europe East Germanic, West Baltic, Continental Celtic, Aeolian Greek etc. are long gone. If anywhere in IE, it is in Indo-Iranian that we should expect to be able to reach quite deep time depths by collecting data from modern varieties and applying comparative reconstruction efforts as usual. Yet this generally seems to have not been done, and approximations derived mainly from Sanskrit and Avestan end up making do as Proto-Indic, Proto-Iranian, and the main fodder for Proto-Indo-Iranian.
By now there is clear evidence that this is insufficient. One informative case from recent years is Martin Kümmel’s observation that “secondary” word-initial h- in several Iranian varieties — at least Khotanese and many western Iranian varieties including Middle to New Persian — actually seems to be a retention of PIE laryngeals (especially *h₂)! This may not have been completely out of the blue. Laryngeal hiatus in Vedic (*aHa > *a.a > ā in some cases still parsing as two syllables) has been known since the early decades of laryngeal theory, and Cheung’s Etymological Dictionary of the Iranian Verb from 2007 takes an extremely cautionary approach of projecting all PIE laryngeals into Proto-Iranian, including an implausible-looking contrast between this *H and secondary Iranian *h < *s (and implausible-looking clusters like *Hhauš- ‘to dry out’).  Regardless we do see that it is incorrect methodology to treat any divergences from attested Old Iranian as innovations, and that this will fail to connect archaisms in marginal new Indo-Iranian varieties back with the wider programme of Indo-European reconstruction. The same has been very patiently explained by Kümmel too, in a 2016 paper “Is ancient old and modern new? Fallacies of attestation and reconstruction“.
I’ve picked Kurdish here as a semi-random example of a modern Iranian language group that probably deserves closer investigation in this fashion, though its western peripheral location might indeed make it a more likely location for archaisms than smaller languages more fully encircled by Persian. It quite clearly shares at least the propensity of retaining *h₂. Even just looking over the lexicon of standard Kurmanji as listed at Wikipedia readily turns up cases like hêk ‘egg’ << PII *Hāwyam < PIE *h₂ōwyom; hirç ‘bear’ << PII *Hr̥ćšas < PIE *h₂r̥tḱos (~ Middle Persian xāyag, xirs). However also cases like hesp ‘horse’, where some kind of “aspiration throwback” could be considered (*asp- > *esʰp > hesp).
The outlines of Kurdish historical phonology are known, of course. Relatively detailed discussion is readily found in sources like Asarian & Livshits (1994), or at Iranica Online. What seems to be missing from these accounts, however, is any real integration of variation among the Kurdish “dialects” (by now widely thought to comprise at least 2–3 languages). They also spend much effort on lamenting difficulties in telling what might be native Kurdish words and what loanwords from Persian or Zazaki or some other neighboring Iranian variety; same as in many other studies on individual western Iranian varieties. But we — at least e.g. us Uralicists — know quite well that attention paid to dialectology is often able to resolve such issues! Maybe some Kurdish variety would turn out to display a form different from the others that would then need to be considered the native one; or to display a different loanword substitution, pointing in favor of relatively recent loaning, whether from Persian or not. Dialect differences could also help with relative chronology, in telling late areal changes (and across Iranian these are many) apart from what really are early Proto-Kurdish innovations. The retained laryngeals, too, are noted by Kümmel to not be entirely systematic. Conceivably it could be the case that e.g. Kurdish only gets them through Persian, at some older or newer date. Or inversely, maybe Kurdish might be in its native vocabulary more systematic about this than Persian is. No way to tell before looking.
Let me be clear here on the proposal. A reconstruction of e.g. Proto-Kurdish should not rely on just some handful of already available descriptions / dictionaries (though I’m sure their comparison, too, would already add up to several results), nor aim just for identifying phonological variation. The goal of such a project should be primarily lexicogeographic: to have detailed enough dialectological picture to be able to see the directions of vocabulary spread, to tell local innovations apart from local archaisms. In Uralic studies, when putting together an understanding of, or at least the data for understanding, Proto-Samic, Proto-Mari, Proto-Permic, Proto-Mansi, Proto-Khanty, Proto-Selkup, etc., we have routinely based this on low double digit numbers of varieties, each documented at least to low quadruple digits of vocabulary. And these are all smallish language groups, spoken by some tens or hundreds of thousands of people. The Kurdish languages have tens of millions of speakers altogether. Even if extensive fieldwork in Kurdistan were to look too dangerous or politically complex right now, already connecting with the diaspora communities worldwide should be easily able to provide data on some dozens of varieties.
I do not pretend that this would be a small or quick task (it is clearly beyond what I or anyone could accomplish as just one unattached researcher), but it seems like a very doable task, and likely fruitful, not just for the circles of Kurdish studies or Iranian studies, but for Indo-European studies altogether. And by no means is this a gigantic endeavor either. This could be all done in under a decade by one research group, if there was first of all the will for it to happen (be funded and prioritized).
Closing up this plea, let me also suggest one other hypothesis that could be up to something. In existing overviews, Kurdish is reported to “sometimes” show PIr. *x > kʰ, e.g. *xara- > /kʰer/ ‘mule’. The facts that this development (1) fails to be regular and (2) seems to be a regression (alleged PIr. free-standing *x is < PII *kʰ) should already suggest that it is perhaps an archaism rather than an innovation. The same might go for /tʰ/ from “PIr. *θ” < PII *tʰ, reported at least in *θaiwar- > /tʰiː/ ‘brother-in-law’. This interpretation is not airtight off the cuff by any means: both Armenian and Semitic influence could have encouraged secondary introduction of aspirated stops. But, interestingly, on a brief look-around I do not find cases where Persian /x/ ~ Kurdish /kʰ/ would derive from a secondary *x that continues *h₂, only cases with PII *kʰ. From the former, the result seems to be /h/, as above in e.g. ‘egg’. So did Kurdish regularly shift *x > /h/, while never shifting *kʰ? Again, detailed dialect evidence could perhaps swing this either way. One of these decades we will hopefully know better.
 Yes, written Sami already existed 200 years ago, indeed since the mid-17th century. The first variety to have been standardized to some practical extent was so-called “Old Swedish Sami”, a clergy-designed form from the mid-18th, based most closely on Ume Sami though aimed as a general western interdialectal standard. Standard Northern Sami took its first steps around the same time as well.
 Omniretained laryngeals are furthermore trouble also for e.g. RUKI. If we have *s > *š in e.g. *buHs- > *buHš ‘to endeavor’, as if triggered by a preceding *H and not *ū, why not also in e.g. *yaHs- > *yaHh- ‘to girdle’? Without the assumption of universal laryngeal preservation, though, this could be easily resolved by assuming *eH >> *ā as an independent vocalization from *iH/*uH > *ī/*ū. Note also a further but welcome corollary: if we do go with thinking that RUKI in *buHš- has been triggered by a long-retained *H, then also *Hhauš- will have to be simplified to just *hauš-, indeed already to a pre-RUKI late PIE *sews- < early PIE *h₂sews-.