I would say no, but I’m doing the exact thing you are (same majors). I think that’s the one exception, because both majors in this case will leave you with the same prospects (for the most part). But otherwise, no. Especially not at NYU where the cost is $70k.
I was about to do the same thing, but I have ended up applying to Gallatin. I think it is worth of doing, but after some time (I really wondered about it) it is not worth when it comes to NYU, which is such expensive school. I do not think so that I would do it, because in the end, the degree matters, and not that much a school that you attend, because some people are very talented but they have no money to attend such a school. I think it is not worth it, but I truly understand you. In my case, I have just realised that I want to combine music with economics, so thus I have chosen gallatin over CAS or very competitive Stern