It's a historical grammatical thing. It's like a "tag" on one word that could be duplicated on another word (agreement of adjectives, verbs, etc. with a noun) so that information is not just preserved but error-corrected in case someone misspeaks or mishears.

Gender is actually a subset of class systems in general and is overblown because of bias towards Indo-European class systems which happen to be mostly along lines of gender.

Yeah I know, not really an improvement if we start calling it a class system instead of gender 😑

To answer your question, I guess a language could break down without this redundancy mechanism of class agreement. But then descendants of European languages like pidgins and creoles often just drop gender altogether and work just fine.