You will need to turn finals a lot higher than 500' to be able to recover a spin.
I agree entirely Cats 5, which is why we don't fly slow in a finals turn.
But in principle I agree with n5296s too. It should be entirely possible to recover from an incipient spin in much less height than that (and is). It's just that a small but non-zero stream of pilots (with spin training) get themselves into a situation where they don't.
Paul