That's my question, if each transformation step preserves semantics, how come they can't apply the optimization on the recursive form? I'm asking seeking clarification.

In general, proving things about recursive functions is more difficult. I could be wrong, but I think for example control flow graph builders usually stop at function boundaries, to keep the problem tractable. Turning a recursive function into an iteration makes it so you can see the whole execution as a single call, instead of having to hop around a virtual call stack.

What I'm wondering is how they're able to turn the optimized form back into a recursive function. Surely there must be some recursive functions that if you optimize them they turn into simple loops or even a linear function is they're very bad.