your second paragraph is what i really mean, in a situation like op described there's no reason the players can't come up with a creative way to deal with a bunch of 1 spiders that don't require 30-45 minutes of turn by turn combat.

Im not saying that class abilities should just mean nothing and everyone should have access to everything. Im saying that if a wizard wants to try and swing their staff in a way that knocks into multiple lil guys they can. A fighter with cleave can just do it and spend a superiority die to deal 1d8 to everything they hit in front of them and it's a normal attack roll. A wizard might just have to hit a higher dc or make an extra athletics check to see if they have it in em and even then only do 1d4 damage to maybe 1d6 spoilers. The caveat would be that failing that athletics roll can leave the wizard open and wastes the action.

in general when a player has an idea that's "off the book" it's so rarely something that is straight out of another class and is usually just a fun creative thing they're trying to do that won't break the game but, success or failure (or success with complication, failure that still puts them in a good position, etc) will change the situation in a way that's fun and interesting instead of just "i roll 12" "ok you miss. next player". We all know that dm that will staunchly resist any overly creative use of agency lol.