If your floor is still solid, and not spongy, there's no reason to take it up. If the floor is particle board, it may come apart if it stays wet long enough. If you can get everything dried out, you might be just fine. There again, if the floor is not spongy or soft, give it time to dry completely. Even if it's spongy under the cabinets, as long as you are able to walk or stand in the middle on solid, you can probably get away with that. Trying to fix may do more damage than just leaving it the way it is. AND, even if the area you walk on is a little spongy, even that's OK, as long as it's not getting softer and softer and crumbling. I'd wait and see how everything dries out before jumping in and tearing the floor out when you may not need to.
If you need to remove some of the floor around the various drains, I'd just cut out only enough to open a hole to make it easier to work, and plan on replacing. Especially if it's under a cabinet. Personally, I think your floor is fine.