Well, yes and no, and no. A properly entered spin in a utility category plane will not become a spiral dive, or that plane would not be certified. Any aircraft for which the spin changes to a spiral dive within one turn of the spin will not be certified without a lot of discussion with the approving authority.
I wouldn't regard that as much of a problem myself given that a spiral dive is easily recovered from in most aeroplanes - I've test flown and certified without difficulty aeroplanes which autorecovered into a spiral dive. I can't think of anything in part 23 which requires the aeroplane to stay in a spin.
It does need some careful POH wording, and there is the issue that most light aircraft instructors and students never read the POH, but that's basically Darwinian and the authorities don't have big issues about that.
G