If it doesn't control both then TCO is impossible, because the stack will grow with each recursive step, as it's just performing a normal call.

Have your mind blown: https://godbolt.org/z/xnn3PPxvW

Extremely specific example is uncompelling.

It is a simple counterexample to your incorrect statement.

It's still impossible in the general case, where not all arguments are passable by registers.

You are right that there are cases where it is not possible. But it also works when arguments are not passed in registers. The condition then is that there are less stack slots used than in the caller.

https://godbolt.org/z/M4Eqzh3YE

It's possible for calling conventions where the callee is responsible for stack cleanup before return.