That is indeed a good point. In any language group with that much vowel qualities, the vowels tend to be unstable. See for example the development of the Romance languages (Latin had different vowel qualities for short and long vowels). And the Germanic languages also offer plenty of examples like the Great Vowel Shift of the English language.
But I'm running into the same problem as everyone. Too little data.. I started looking into this because I wanted more data for my vowel model, especially the development of the laryngeals. But I find Indo-Uralic interesting in its own right. And getting more data requires a lot of time. And better dictionaries. For example, Uralonet (UEW) is great for searching, but their reconstructions are problematic. I'm still wondering what they mean with O-breve and O-breve-umlaut. For now, I just replace that with a schwa in my data.
Also, even if someone makes a Proto-Indo-Uralic reconstruction, it won't mean that everyone will suddenly see PIU as a real thing. It will probably end up in a situation similar to Proto-Altaic. Yes, it is possible to make some reconstruction, but how much **akwater will it have?
One example of why I'm not at all optimistic is PU ś.
I think it corresponds to PIE consonant clusters involving s, like sk, sp, st:
PU: śota, śoδa, śoδ̕a 'fight (n), struggle, war; fight, struggle (vi)' UEW#1597 FW
PIE: sperdʰ 'to compete, contest, struggle'
PU: śakkɜ (śukkɜ) 'piece, bit, part ' UEW#924 Ug ??FU
PIE: (s)tewg- 'to break, piece' (cognate germ. Stück)
PU: śu-re FW 'mush, groats, pulp' UEW#1601
PIE: (s)poH(y) 'foam'
But with the IE s-mobile phenomenon, this means ś can correspond to anything.
And then you can make correspondences like:
PU: śiδä (śiδä-mɜ), śüδä, śüδä-mɜ U 'heart ' UEW#960 U
PIE: ḱerd 'heart' from earlier **sḱert ??
(or PIE: psten 'breast, teat')
PU: śänčɜ 'knee ' UEW#949 U
PIE: kenk ‘knee-cup, heel’ from earlier **skenk??
PU: śulɜ U 'vessel ' UEW#982 U
PIE: pel 'container, vessel, dish' cognate Latin pelvis, from earlier **spel??)
A couple more sound changes like this, and critical linguists will be tearing PIU to pieces.