2. There are very few knobs you can tweak to control how your call stack space is allocated or represented in memory. With a stack container, you have much finer control over that - you can do reallocations or define custom error handling when you overflow the container, you can deallocate/shrink the container when you no longer need the space, you can serialize the container to disk to make your processing resumable, etc.
3. A call stack has a very limited set of operations. You can only access data from the current stack frame, and you can only push/pop (call/return) stack frames. But with your own stack-like data structure, you could extend it to do far more, e.g. accessing data from the first or last n traversals, or insert/remove multiple elements at once.
If you’ve formally verified that function X uses at most Y pages of stack, and the remaining stack is smaller than that, you could return an OUT_OF_STACK error instead of calling it. Most libraries/functions wouldn’t need this, but there are C libraries which place an extraordinary importance on reliability, and it seems like it would be a useful feature for them.
There might be other reasons why these functions shouldn’t be in the standard (or are impossible on some platforms), but ”the information is worthless” is not one of them. Of course this information can be useful.
There are more hacks in Heaven and Earth, Horatio, than are dreamed of in your philosophy.
Moreover, every nontrivial C program in practice contains UB.
Nevertheless, it does matter what is and isn't standardized; standardizing such functions would greatly improve the situation for programs like those I mention, because they would be able to rely on the C standard to find out when they're about to run out of stack, an event they already have code for handling. It's true that a pathological C library implementation could still totally break their stack-exhaustion-handling code, and in fact that's already true, but fortunately there are lots of C library implementations that behave well enough in practice.
The meta-problem is what to do with the information.