Diphthong Distributions

I was looking at some PIE roots today and noticed some interesting
distributions of diphthongs.

1) Roots in *tei- are nonexistent
2) Roots in *weu- are nonexistent
3) Roots in *yei- are nonexistent
4) Roots in *gW(H)eu-/*kWeu-/k'weu- are nonexistent

However,

5) Roots in *trei- exist
6) Roots in *stei- exist (here s- can, but doesn't have to be, s-mobile)
7) Roots in *wei- are common
8) Roots in *gW(H)ei-/*kWei-/k'wei are common

I didn't look at any roots with diphthongs of o-vocalism.

I think (1) is indirect evidence for an early sound law, *ti > *si, if
we assume that *ei < *i. This sound law would also explain why the
second person is sometimes represented by *t and other times by *s. In
pronouns, for example, we have *tu. Yet for verbs the 2nd person
singular subject agreement marker is *s which would presumably derive
from *-ti with loss of the final vowel. Perhaps this could explain the
anaphoric pronoun which has a *t~*s alternation. This fits with (5)
because the *r prevents the assibiliation. Similarly in (6) the *s
would prevent the assibilation. If this line of reasoning is correct
then the s-mobile must have been an original phoneme that was later
lost for whatever reason, as opposed to a prefix.

(2) and (3) could be explained in a couple ways. Roots in *weu and
*yei did exist but dissimilated to *wei and *yeu respectively. Or
perhaps *y and *w are allophones with the above distribution. I would
tend to go with the first because it might open up a can of words for
other things, though I haven't really thought about it. If we
re-analyse *ei < *i and *eu < *u then are there any roots with *w or
*y root final? I guess these could be the i- and u-stems, but maybe not.

(4) and (8) could be explained by the same dissimilation effect as
above. Both *eu and *ei diphthongs seem to appear with roots beginning
with velars and palatals. This could be interpreting as supporting the
notion that palatalization occurred after the assibilation and
dissimilation stages.