My past bass instructor, who happened to play on lots of NYC Broadway shows, once told me that a fretless bass is treated as a whole other instrument on a Broadway show, similar to the difference between any two distinct instruments. Players who are asked to play fretless, as well as fretted, are paid more money, as are players who might play clarinet and tuba parts on a show.
Just that piece of information made me feel OK about never being able to get used to playing fretless. I could only do so on simpler songs that I regularly gig. Since I didn't use my fretless that much, I sold it a couple years ago.