By assuming the linear approximation is good enough, you beg the question. Consider that if that is to be assumed, you could just take U, A and B to be linear functions to begin with...

It's not so much an assumption, as an intermediate conclusion that follows from the dependence of U on A and B being smooth enough (across the kind of change that dM is capable of making) and nothing else. My only claim is that under this assumption, the non-diversification conclusion follows. U(A,B) being linear is a hugely more restrictive assumption.