If SCT is false then for example it may be possible for a quantum computer to use an uncountable set of inputs to compute in finite time whether an arbitrary turing machine will end.

That said, you're right, if all that is required is real numbers, then hypothetically an analog computer is all that would be required. But in a truly quantum world where SCT holds, an "analog" computer is only a computable approximation.

(Full disclosure: I guess....)