You're alluding to using the Morris traversal algorithm which can traverse a binary tree in O(1) space, but Morris traversal is actually much much slower than using a stack, especially as is used by this algorithm. Doing a Morris traversal requires at a minimum twice the number of operations as using a stack, and due to its cache unfriendly nature will in practice be closer to 4x slower.

You typically only use Morris traversal on exceptionally large trees, and by large I mean when working with data that lives on a disk. It's definitely the exception, not the norm.