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.
It should be, indeed it is at altitude when there isn't the pressure of being in the circuit and planning a landing. As you so rightly say, if one doesn't fly too slowly one isn't going to spin and the problem with all the near the ground stuff, and with the rising horizon stuff, is it can sucker the unwary into slowing down.