It's not one I endorse using when what someone has said isn't right.
To the extent that "X, but Y" is understood to mean (not-X and Y) it's a broken form of communication; to the extent that "X, but Y" is understood to mean (X and Y) it's false when X is false; to the extent that "X, but Y" is understood to mean (Y and (X or not X)) it is strictly worse than "Y".

Then again, I once got the feedback at a meeting that I was the only person the speaker knew who could say "Everything you just said is absolutely correct" in a way that left completely unambiguous the implicit "...and you're a moron," so there may well be a huge gap here between what I endorse and my practice. In my defense, though, everything the speaker had just said was absolutely correct. (It was also entirely irrelevant to the thing I'd been talking about.)