if all theories can be re-presented as consequentialist, then it means little to label a theory as consequentialist. Even if successful, we would then have many different ‘consequentialisms’ that suggest, in practice, different things
I think this is very much answered in the post, by the analogy to limiting cases:
Sometimes, the relation between theories in physics is that one theory can be understood to be a special or limited case of another theory, for example a low-energy limit, high-energy limit, or classical limit. In these cases, the theory covering more of the territory can sometimes tell us when we can safely use the simpler, limiting case theory.
The claim is not “all these theories are equivalent despite arriving at different conclusions”—but rather “these are what consequentialism boils down to under the assumptions that are in fact relevant to us most of the time”. Different limiting cases can have contradictory results, but that just means you need to know which one is a good approximation for your case and which one isn’t.
I think this is very much answered in the post, by the analogy to limiting cases:
The claim is not “all these theories are equivalent despite arriving at different conclusions”—but rather “these are what consequentialism boils down to under the assumptions that are in fact relevant to us most of the time”. Different limiting cases can have contradictory results, but that just means you need to know which one is a good approximation for your case and which one isn’t.