But this conflates two very different language requirements in one feature: the need for nested (unbounded, if your language isn't broken) function application, and the need for diagnostics of dynamic errors.
The first is what continuations and stacks are all about, of course:
Now, as it turns out, it's a pretty useful source of information. And if you happen not to have proper tail recursion, it's even more useful, since it provides a path through the function call graph. But I've been finding stack traces in Scheme less informative, because with proper tail calls, there's less function-call history in the continuation.
I recognize that sometimes the "complexity budget" in language design necessitates using one feature to satisfy multiple requirements. But I'd like to see more investigation of linguistic diagnostics designed independently of existing language features. For example, it might be useful to provide configurable tracing facilities that record program history during runtime, where the tuning of how much gets recorded is completely independent of the space semantics of the evaluator. So you have a properly tail recursive semantics with a flexible tracing facility grafted on top.
What classifies a language feature as "purely diagnostic" might be that it is designed not to change the observable behavior of the program, but merely to report some additional information. Contracts-as-projections is an example.
Update: rephrased my rookie characterization of continuations.