This is a bit misleading -- desirable over what? I could say anything is desirable if I have in mind to compare it with something less desirable. Also, saying desirable is not a statement of best. Are you claiming a Ph.D. in math or economics is better than any other Ph.D. you could earn?
Are you sure a Ph.D. in philosophy (game theory), physics (learning how to model reality...), or engineering (signals & systems; machine learning; learning how to model reality) would not be superior over either degree? Do you need to know how to prove the fundamental theorem of calculus to apply calculus effectively? Physicists and engineers learn to use mathematics well without the concern of proving it. I desire the practical skills from physics or engineering over the abstract, pedantic approach by mathematicians.
I'd think Physics is just as good, perhaps better than mathematics in terms of city desirability, but it depends on the role. As you mention it's exactly about the skills acquired from doing the PhD more than the knowledge set.
If you do a PhD in mathematics, you'll probably be well be practiced in logic and logical thinking, basic probability and expectation, attention to detail, perseverance in the face of failure, pattern recognition, focus, abstract thought, handling data, maybe programming experience, plus you can fairly quickly pick up any of the financial maths for options etc.
Well there are more, but those are the ones I can think of that are relevant to trading. I don't think a PhD in philosophy or history etc will give you as good a list of desirable skills, but I could be wrong. Physics will. Engineering, depends. Being pedantic is a good thing in trading anyway isn't it?
Then again, some people have these skills without ever doing a PhD. And some people have other skills that are more useful to trading than those above. But those are harder to detect on a written CV.