That seems to be the same as 'no computation can output a prefix that is sufficiently long to be useful in predictions'?

This would depend on how long a prefix you need. If there exists a constant K such that K-length prefixes of all universal constants are enough, then certainly all possible bitstrings of length K can be computed.

The question becomes: what does a universe look like where you need to know the exact value of some constants to make useful predictions? (Perhaps you can make some predictions using approximations, but some other possible scenarios remain unpredictable without precise knowledge.)

This requires knowing an infinite amount of information: some kind of physical reification of an uncomputable real number. (I'm only using real numbers as a familiar example; larger infinities could be used too.) Not just to know the constant, but probably also to know the precise initial state of the system whose evolution you want to predict.

One possible reification is the precise position, mass, momentum, etc. of an element in the simulation - assuming these properties can also have any real value, and that you can control them to that degree.

I feel I could still imagine such a universe. But either way that's a fact about me, not about universes. I don't know how to predict the measure of such universes in any multiverse theory.