This page does not identify an algorithm that can be implemented in fixed space but is hard or impossible to do with tail recursion. No such algorithm exists. It is unclear which of the dozens of beautiful algorithms it presents you mistakenly believed to be one.

tmtvl's comment at https://news.ycombinator.com/item?id=41983916 shows an algorithm that requires unbounded space.

Traversing a mutable binary tree can be done in fixed space but is not easier to do with generalized forms of recursion than with tail recursion or imperative iteration.