That way you don't go through an MSc program for no reason (other than perhaps picking up the additional classes).
Just going through the program is not the point. The point is to tailor the program to be about practical stuff. At the moment, his CV is lacking on the practical side. Is this not something to consider? I think that would still be an issue even with a PhD. Like I said, no one really trusts a pure theoretician. I question whether sparkling theoretical stuff can outweigh the perception that there is an issue there with practicality.
Other threads on the same topic have suggested that a second Masters won't help because anyone would do well doing a second Masters, so what does it really say? But when your first Masters is saying, "I stuck my head in a book because I couldn't handle the rigors of practicality", that is a red flag to me.
If it is the case that having a PhD means no one looks at the Masters, then it is okay, but I suspect that it's not true and people do look at past results. The good must counter the bad. If a PhD can do that, then okay. But at the moment, I'm seeing someone who IMHO underperformed in the Masters. And even being a PhD, how one did as a Masters student would seem to say more about the practical than the actual PhD. If I'm wrong in this point, I will hold my hands up and apologize. And please step into correct me. But if I'm not wrong, it would help the OP to flush out the weakness that is not proven to be an issue but may turn out to be one. Now is the time, right?
You want the best CV possible. At the moment, he is not competing as a Masters, IMHO. He can do the PhD but he needs to compete then as a PhD and this Masters performance is always there, is it not? At the end of the day, no one should think that school isn't about getting the best result you can. It is about learning skills and this does count, but you are there to achieve and do well. IMHO, OP dropped the ball somewhat, it's not terminal by any means, but there is a perception there and a second Masters could correct it. And he was already thinking about a second Masters, although having it be all about pure theory (QFT, etc) is, I believe, missing the opportunity of eradicating this perception for good.
Perhaps I can package-deal it. A second Masters could be worthwhile if it demonstrates that you are competent practically and can be trusted to get on with it and produce high-quality output. I don't see how that could be bad. A second Masters could fail to be worthwhile if it furthers your knowledge but leaves the practicality issue dormant.