I've never used a mute (just palm), but I've always liked the idea. If I were doing any sort of beatles/motown style project, it would almost be a must. That said, for occasional muting, I don't think it makes sense, they can take a while to set up, thus the decline in their stock availability.
That said, I played about 10-15 musicmans a month or so ago at gc and a few local shops around here, and I thought they all had the built in mute bridge, or at least a couple of them did. One shop I visited had a vintage (late 70's if I recall) sting ray, and yes, the foam was pretty badly degraded. Looked like an easy fix.
So if several sting rays are not music men, would several bass players using sting rays be music men?