When I looked at words in Proto-Indo-European and how the words evolved, I found that there aren't a lot of words in that proto-language and that the words appear to be somewhat shorter than those in English. I am wondering if it has to do with limits of comparative recovery of PIE vocab, unsophisticated word choice, or a combination of both. Also, the words do seem to be somewhat limited in variety.
The vocabulary of PIE must have been larger than meets the eye.
By rough estimates, a language could meet its semantic needs with as few as 3,000 independent roots and their derivatives. Most languages have twice that many roots, but many roots are borrowed and many are rare. (For example, Hans Wehr’s Dictionary of Modern Written Arabic lists about 3,000 roots, but searches of old lexicons find over 6,000. Chinese students must learn 5,000 characters to read proficiently. Panini’s Dhatupatha lists 2,000 verb roots alone in Sanskrit, but only half are actually found in texts.)
Pokorny catalogued about 2,000 reconstructed roots, but many items in his lexicon seem shaky, either for lack of solid attestation in multiple branches of the IE family, or for too-loose semantic connection with alleged cognates, and some seeming cognates may actually be loanwords. By conservative estimate, only one-third of Pokorny’s material is beyond question.
We might try to work backwards from 750 well-attested roots. Glottochronology has estimated the rate of vocabulary replacement at 14-19% per thousand years. Using the latter figure, we would expect half the PIE roots to be preserved in any given major branch after 3,500 years. With five major branches (indo-Iranian, Greek, Italo-Celtic, Balto-Slavic, and Germanic), the probability that a given root would have been lost entirely is very low. But any figure between 750 and 1,500 roots is hardly enough.
Where might glottochronology have gone wrong? Swadesh’s widely cited estimate is based on a list of only 200 widely distributed words, but rare roots may have higher rates of replacement.
And where might lexicography have gone wrong? An unknown number of roots may actually have survived in one branch or another but still be lost to history for lack of identifiable cognates in other branches.
It is pretty clear that the size of the Proto-Indogermanic vocabulary is limited by the method of reconstruction. Since the most frequent words of a language tend to be short and frequent words have a better chance of preservation, there is a bias towards short words in reconstruction.
Another factor is that we know that Proto-Indogermanic has had some derivational morphology that was productively used, but dictionaries are concentrating on roots and just the derivational morphemes and don't list the derived words. Reducing the language just to roots and morphemes may give a wrong impression on how the language actually looked like. For a better illustration, look at some made-up Proto-Indogermanic texts like Schleicher's fable.
My impression is that the vocabulary of PIE was quite large. We already have a lot of roots to conclude that it had at least not less roots than Latin or Greek.
In addition it had a lot of suffixes that could modify the meaning as well as compound words, similar to German.
And the words definitely were not shorter than in English, they were much longer (you should not confuse roots with words).