I think Zipf's law means you're biased towards odd in that case (unless you allow yourself to choose empty strings)
However, I think you're correct anyway. The right distribution to look at is something like the orange series in the bottom graph on [0]. Eyeballing it, it does look like 3/5/7/9/11-letter words appear more in aggregate than those of 2/4/6/8/10 (49% Vs 44.5%), and longer words are a rounding error.
[0] https://medium.com/@davidxu90/relative-frequencies-of-words-...