Yes, but it's more nuanced than that. Even if you can prove that a computation always terminates you can't necessarily prove that it yields the wanted result in any reasonable amount of time. This is the bounded halting problem, and it applies even to languages that only allow terminating computations. In those languages, the halting problem is nominally gone, but the bounded halting problem is just as bad as for Turing-complete languages. Just how bad is it? It is a time complexity class that includes all time complexity classes, i.e. it is harder (in general) than any problem that is computable and known to complete within f(n) steps, where n is the size of the input and f is any computable function.