I would disagree that even used disingenuously that one can win any argument. If one has a solid case, where the conclusion logically follows from the premises, all it would really do is disect the argument back to the premises. If you break it down the the premises and they’re solid, meaningful premises, then the disingenuous socratic arguer basically just walked you through proving your case.
Look at it from a mathematical perspective. Every proof is based upon previous proofs but eventually can be traced back to some fundamental axioms. Sure, once you get to those axioms, the why stops because because of some previous statement and just becomes the simple argument that if you reject those axioms, you’d essentially have to reject the entirety of mathematics.
Obviously, it’s not going to be that big in a lot of cases, but really, when you get down to it, that’s what a lot of arguments are. Either one (or both) is making a logical mistake between their premises and their conclusion, or the two people disagree on the validity of the premises. So following the socratic method would just eliminate the first issue. And, if you agree on the logic and agree on the premises, then you can’t disagree with the conclusion in good faith.