Whats on the back side of the valve? Is it a wall you can easily cut out and repair or is it a nightmare of cabinets on top of tile or an exterior wall?

If it's easy to cut out and repair, like a simple Sheetrock and paint job, then that might help determine what you want to do. Personally I loath dual knob showers so I would try to install a new faucet if I could but I'm not sure I would go so far to rip out tile to do it. I would however open up a hallway or bedroom wall in a heartbeat.

They make shower cover plates that would convert your existing 3 hole setup into a single hole setup so that's an easy fix if you do go with a single knob mixer.

Also, if you do rip out the back wall, if practical, you could consider putting a small door in the wall for the next guy who might want to replace it. Sometimes that next guy is you.