They don't get an s because that's not what they're called.
300 is called three hundred. That is its name. You could say you are counting the number of hundreds, but you're not really, you're just naming something. We could have ended up calling it thirtyty, or something, but we haven't.
Also you can say 3 hundreds or 2 thousands, when you are counting them.
I have 3 hundreds, 14 fifties, and 12 ones.