A language tends to work as a organic whole, so taking one element (e.g. whether pronouns are gendered or not) in isolation and arguing that if one language doesn't do it, another language doesn't need to do it either, is a dubious undertaking without a thorough knowledge of both languages concerned.
An example: if you want to explain a situation involving Jane, Susan, cake and giving, in English, you do it with word order and a preposition: "Jane gave the cake to Susan".
You can't reverse Jane and cake without changing the meaning - "the cake gave Jane to Susan"(!).
Even moving "to Susan" feels a bit off - "to Susan Jane gave the cake" because although the meaning is still clear, word order is so strong in English that we are sensitive to word-order oddities. (It might sound ok if we were narrating how Jane gave various different things to different people, with the emphasis on who got what; in isolation it sounds awkwardly phrased.)
In Latin it would be a different matter, because Latin nouns have case endings. Jane (the subject doing the verb) would be in the nominative, the cake (object of the action) would be accusative, and Susan (recipient) would have a dative case ending. So wherever you put them in the sentence, their grammatical function travels with them and meaning isn't lost, and word order can be used purely for emphasis.
Along comes Innovatus Optimisticus and says "Hey, guys, some languages don't have case endings, we don't need this shit!"
Sure, they don't, but if they ditch them, it's not "just" a matter of ditching case endings. It has implications for how Latin handles word order and emphasis, and possibly other things too that I haven't thought of (it's a long time since I did any Latin).
Similarly with pronouns and gender, I suspect.