I think to some extent the point is disambiguation while allowing for a greater flexibility in word order. At least in Latin, a lot of the poetry (especially by that fucker Catullus) has the most insane word order that without matched genders and cases of adjectives+nouns simply wouldn't make any sense. Or at least couldn't guarantee it's going to make the sense the author had intended. Having said that, as
>>2 said, languages do just fine without it at the cost of more strict rules determining word order. This is especially true of Chinese, much moreso than Finnish; Finnish still maintains a complex albeit logical case structure which allows adj+noun matching. This is also why Chinese poetry is a bitch to translate, it gets very ambiguous and unclear very quickly.
I personally think gendering nouns is generally silly and only workable when words comply and without fail to a series of clear rules. Latin didn't manage to do this properly though, with a bunch of genders and then declensions and then the exceptions thrown on top of that. Even Esperanto, a completely constructed language couldn't figure out a comprehensive and foolproof way of doing it - whether that demonstrates a failure in the concept of gendering nouns or just the execution is up to you though.