Should I be breaking cave spider spawners in Minecraft?

So I'm exploring an abandoned mineshaft inside a ravine and I keep running into cave spiders. I've lit the spawners but I'm wondering if I should break them just to make sure they don't spawn anymore because they're really annoying

That must be one hell of a cave.

There's always that small chance that stuff can still spawn even if you cap the spawner (torching it on all sides and around it if need be). But is there a lot of em still popping up? Maybe there's another one nearby or something…

You can try and see what happens

Most players & servers prefer NOT to break spawners in general as they're permanently destroyed in the process & removing a potential resource. They prefer to just use torches to disable the spawner so that can potentially re-enable it once they have the mechanics to harvest the mobs.

Please be aware that it's very possible to have multiple spawners in a small area. I've ran into this where the world generated 2 spawners within about 16 blocks of each other in an abandoned mineshaft. Therefore, if you still see a stream of cave spiders after disabling one spawner, proceed cautiously & look for another one.

HOWEVER, the choice is ultimately yours on how you want to proceed. I just prefer not to take unreversable actions unless I'm willing to live with the decision.