I actually find this aspect of the game frustrating. Frustrating enough that I'm not sure if I'll bother keeping this game in my regular schedule. It shouldn't matter when I do it, the same answer should be the same score.
I dunno how you would score it in that way, because the current scoring system is pretty elegant in conception. Maybe using Ngrams or something?
Couldn't you just measure against the general occurence of a word in online texts? Whether a word is rare or not shouldn't be dependent on people's answers, should it?
an online search engine that charts the frequencies of any set of search strings using a yearly count of n-grams found in printed sources published between 1500 and 2019
Basically: how popular was it to use this word or phrase in all recorded text available to the search engine (including scanned old books), charted over time.
There's technically a slight advantage because someone hunting for rare words might move off of your word because it is not a unicorn. However that is only true if you go back to your puzzle later and fix any words that went down in rarity, if you aren't going to do that then playing later is probably better.