Obviously I don't know about anyone else. But, if I were recording, I would want the sound to be "my" sound. Obviously, things like weight wouldn't really matter for recording. In other words, what I used to record would likely be my favorite bass (at least, for whatever type of music I was playing).
Stingray 5s are notorious for being heavy. But, there ARE light ones out there and if that was my favorite bass and "my" sound, I would definitely find a light one for road work - even if it didn't sound quite as good/the same, as my favorite one, which I used for recording. I might even go as far as having somebody like Pat Wilkins cut the top off, chamber the body, and put a new top on, just to get it light enough, if weight were really a factor for me.
The only reason *I* could see for using a completely different bass, with a completely different sound, for road work would be some kind of business obligation. Weight is "fixable" without going to the extent of changing to a completely different kind of bass.
But, that's just me.