By “physically sensible,” what do you mean? When I say that, I usually mean something that my brain is good at modeling,
It’s hard to put my finger on this exactly. To me, physically sensible just means it sounds reasonable under the context of observations and everything else that we know. In this specific case, the idea of infinitely many universe branches constantly forking off doesn’t seem physically sensible to me when all we observe is a single universe.
In what sort of situation would you expect a correct theory to not be physically sensible?
This just happens all the time. For example, to get the free-fall time for a falling object, you have to take a quadratic root of an expression, which in principle gives a “negative time” root/solution. This solution is obviously nonsense, so you just discard it and don’t pay attention to it, but you don’t conclude that the theory is wrong.
First of all, I disagree that the negative time solution can be removed using math; the math will tell you that the solution is perfectly valid.
Secondly, yes, there are cases like in statistical mechanics or basic QM where the theory isn’t that intuitive, dealing with huge numbers of particles (as in SM) or dealing with position probabilities (as in QM), but where the process makes sense (I can grok it).
But these theories have clear interpretations in terms of observables; SM has a systematic justification in terms of physical intuition (in terms of the preferred configurations being those with the most probability, or something of that nature), and QM develops right from the beginning how the wave-function picture can be seen as a generalization of the classical picture (positions directly become position operators, as with momenta and so on). There’s no such obvious justification for the MWI, in my mind; the linkage between there being many branches of the solution, and there being many universes, is weakly justified at best.