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Godel's incompleteness theorem indicates illegal states as unrepresentable is impossible at a fundamental level.

Well, no, it indicates that it is sometimes impossible at a fundamental level. That doesn't speak to whether it's a good idea some of the times when it is possible.

This is a misinterpretation equivalent to saying "The halting problem indicates it is impossible to say if this loop terminates: while true: break "

It is true that it is impossible in general, but that says nothing about whether or not it is possible in almost every useful case

I sometimes wonder how big the category of "programs that break (or rather, cause) the halting problem" really is.

If we carve out "programs that run themselves on themselves and then do the opposite", what remains?

You both rather miss the point that the op ref talks of making illegal states unrepresentable. An objective that either depends on only handling simplistic data or ... most likely is impossible.

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