At any time a coroutine switch could happen, doesn't the compiler statically know how many registers would be allocated by this anyway? Register numbers aren't

At any time a coroutine switch could happen, doesn't the compiler statically know how many registers would be allocated by this anyway? Register numbers aren't dynamically indexed, they're baked into the instruction stream, so there's not really any new information you can't get from the instruction pointer and a static (compiler-generated) lookup table?