> But when we're talking about the space of all programs, the fundamental limit of incompleteness is important.

I agree with this. But I think that usually we are not really talking about all programs. We are talking about useful programs, and those are usually terminating. In theory, not always, see first-order theorem provers; but in practice, we always call a prover with a time limit because nontermination isn't useful.

> Programs exist before you type them, type systems tell you how they behave. They also tell you how to construct programs but this is subordinate to the more fundamental descriptive capacity.

That's an interesting point, and I agree in many respects. I think when programming in a dynamically typed language, I approach things in one style, and in statically typed languages in another style. But specifically for termination, I don't think so. I never want to write a nonterminating program; the termination property for my programs exists (as a requirement) before the program does.

That's what the escape hatches are for. In Coq, for instance, you can also write functions processing infinite streams, provided that they also produce something regularly. For example, in a game, you could write a function from an infinite stream of inputs to an infinite stream of frame updates. You can not write functions that would not terminate while computing the updates for some given frame.

Alternatively, you just write a function to iterate your game world update N times, where you choose N large enough to ensure that your game can run until the heat death of the universe. That's not a nonterminating function, but it's long-running enough for all practical purposes.