We cannot compute exactly what happens because we don't know what it is, and there's randomness. Superdeterminism is a common cop out to this. However, when I am talking about whether something is computable, I mean whether that interaction produces a result that is more complicated than a turing complete computer can produce. If it's random, it can't be predicted. So perhaps a more precise statement would be, my default assumption is that "similar" enough realities or sequences of events can be computed, given access to randomness, where "similar" is defined by an ability to distinguish this similulation from reality by any means.
Say for instance that you could arrange quarks in some way, and out pops, from the fabric of the universe, a way to find the next busy beaver numbers. Well, we'd be really feeling sorry then, not least because "computable" would turn out to be a misnomer in the formalism, and we'd have to call this clever party trick "mega"-computable. We'd have discovered something that exists beyond turing machines, we'd have discovered, say, a "Turing Oracle". Then, we'd be able to "mega"-compute these constants. Another reason we'd really feel sorry is because it would break all our crypto.
However, that's different than the "idea of Chaitan's constant" existing. That is, the idea exists, but we can't compute the actual constant itself, we only have a metaphor for it.