> that would still IIUIC just get you primitive recursive functions (i.e. those where you can know the upper bound on the number of loop iterations for any loop before it starts)

The primitive recursive functions cannot be expressed using circuits. Circuits by definition can only express polynomials, which have a much smaller growth rate than what primitive recursive functions are capable of.

[edit]

Actually, probably a better reason is that in primitive recursion, the running time can depend on the input. For a circuit, the running time is independent of the input.