TCO isn't about recursion; it applies to any function call in tail position. Some toolchains only manage to avoid over-allocating stack frames for self-recursive tail calls, but that isn't full TCO, and it doesn't help for other interesting case like mutual recursion, state machines, or continuation-passing style. Compilers which compromise on full support for TCO emit programs with built-in memory leaks; they fail to free data which is no longer needed, and thus unnecessarily exhaust their stack allocation.
Programs which use built-in iterative constructs are still recursive; all that "recursion" means is that the control flow folds back on itself. A traditional "while" loop looks like: (1) stop if a condition is false; (2) otherwise do something; (3) do it again. The "it" in (3) is a recursive reference to the loop.
Now, unstructured explicit recursion is barely better than unstructured "goto", so I'm not advocating that everyone start using tail calls in place of loops. However, bare loops are in much the same position with respect to higher-order primitives such as non-strict folds—and those higher-order primitives are much easier to implement in environments which properly support TCO. Languages where TCO is not customary tend to suffer from a proliferation of built-in constructs—iteration, generators, list comprehensions, coroutines, and the like are all implemented as language features requiring custom code generation, where another language where TCO is customary might relegate such primitives to a library.
There are some recursive structures that are just much more natural than their iterative counterparts. Parsing (as lysium suggests in the sibling post), for example.
But also things like graph and tree traversals, and many search algorithms related to those same structures. If you attempt a tree traversal iteratively, you have to maintain the return stack manually, rather than permitting the language to do it for you (assuming a full traversal and not a search, a search could be done iteratively without much trouble).
The "function" in "functional programming" refers to mathematical functions, which are fixed mappings from inputs to results with no side effects. If your "functions" can have side-effects then they're not functions, they're procedures. Programs composed of effectful procedures are imperative, not functional.