Yes, tail recursion can be optimized. But tail recursion is a very limited subset of all possible recursions, and it is also a very limited subset of things that can be implemented in O(1) memory with an iterative loop. It's not obvious that all the things you can do with an iterative loop can be transformed into tail recursion in O(1) memory.

This very thread contains this example: >>37,39,40. I don't see a resolution for how to do foldr with tail recursion. With a loop, I can trivially change the order I traverse the elements in, including some pretty non-trivial orderings like taking the odd elements first and the evens second.

What I asked for is some proof that all this, and not just a subset, can be transformed into tail recursion in O(1) memory and O(n) time.