That still sounds like it's going to make monster-design creativity pretty sharply limited. Maybe I'm just expecting rather high standards here, given the phrasing. Still, if you have to see and fully understand 3-4 abilities a monster has before you can even begin to identify it, I wouldn't see that as being a particularly good "abilities = identity" thing. I should think it would be much quicker than that. Especially since that means you can only really change one ability, if that, and still preserve the monster's identity. If an Ancient Red Dragon is identified by (say) fire breath, whirlwind (from its wings), a tail swipe, and a pillar of fire type thing, you're really only going to get to play with maybe one of those attacks without compromising its identity--and even that's going to be dicey, since if it doesn't get a wing attack (for example), it could be a salamander, whereas if it doesn't get a breath attack it could be a balrog. Etc.
When you can only count on getting 3-4 rounds to work with, and abilities are supposed to conclusively identify what you're facing, there's a pretty sharp limit to how much you can express creativity or monster uniqueness without breaking the bijective map between abilities and identities. But if you have to have it so that each distinct monster can be identified from just one or two category-specific things, e.g. dragons get breath attacks, now you're limited from the other direction, because you can't ever give anything a breath attack without people thinking it's some kind of dragon.