Doesn't sound too good to me: You would limit the number of threads in HW or your OS kernel would have to revert to the conventional context switching - with the additional overhead of checking if there's enough HW resource. You would also have to design/manufacture/pay for HW for the high (constant) number of threads even if your particular application would use only a fraction of those.
Many CPU architectures support alternative register sets for interrupt handlers (ADSP 21xx and ARM come to my mind) but that's not exactly what you're talking about, it's far from being generic.
Some RISC architectures support a moving window over their register bank (I don't know the right term) so that the caller and the callee can work on a different set of registers, thus implementing some limited stack in the registers. That's also somewhat different from your idea though.
Regards, Andras Tantos