N.B. The email exchange below may have been edited, e.g. to remove content not essential to the main point(s) or to standardize English spelling/grammar.
I would like to ask... a question, [for] which I have not yet found any answer, [including on] your website.
Why is the influence of the laryngeals h1, h2 and h3 shown only on vowel 'e', although vowels were two: 'e' and 'o'? For example: h1es, h1ed, h2er, h3ew, dheh1, steh2, deh3 etc., but nothing such as h1oC, Coh2,... etc.
For example, could not the PIE stem doo- ('oo' = long 'o'...) come up from doh- instead of deh3-?
Thank you for you answer, M. L.
You conflate two widely different time-frames; that is, just like any language evolves over time, Proto-Indo-European evolved over time. There is no reason to suspect that the evolution of all PIE ... vowels occurred at the very same time.
W.P. Lehmann's book Proto-Indo-European Phonology is on our website (perhaps you never saw it?), and in it he devotes a chapter (3) to "The Laryngeal Theory." In that chapter he remarks, "Saussure also assumed that all IE roots had a basic vowel e... Other root vowels..., Saussure explained as derived from a laryngeal." Hence (per later formulations of laryngeal theory), the vowel 'o' evolved from the basic vowel 'e' (plus an adjacent laryngeal) [which then disappeared].
Therefore you must reconsider your statement, "vowels were two: 'e' and 'o'." [At some point in time, probably so; but at an earlier point in time, not so. Indo-Europeanists may cite PIE forms from earlier or later times.]
As an aside, there is no reason to expect that all other vowels must have evolved at the very same time; that is, 'o' could have evolved before... others, as laryngeals variously disappeared...