Pre-1.0 Rust used to have infinitely growing stacks, but they abandoned it due to (among other things) performance reasons (IIRC the stacks were not collected with Rust's GC[1], but rather on return; the deepest function calls may happen in tight loops, and if you are allocating and freeing the stack in a tight loop, oops!)
1: Yes, pre-1.0 Rust had a garbage collector.