It's certainly possible on some systems. Even then, you have to fudge, as you don't know exactly how much stack space you need to save for other things.

Stack memory is weird in general. It's usually a fixed amount determined when the thread starts, with the size typically determined by vibes or "seems to work OK." Most programmers don't have much of a notion of how much stack space their code needs, or how much their program needs overall. We know that unbounded non-tail recursion can overflow the stack, but how about bounded-but-large? At what point do you need to start considering such things? A hundred recursive calls? A thousand? A million?

It's all kind of sketchy, but it works well enough in practice, I suppose.