Those escutcheons should pull away from the wall. Then you only have to cut for the water line and when you push them back they will cover it up. They may have been pressed up against wet paint and are now stuck.

Although I do agree with everyone else that removed bge those crappy valves now is the best option long term

Escutcheons are the plastic caps against the wall that prevent you from seeing the hole for the water lines and drain pipe. I’ve never seen this exact setup so they may be threaded into the drywall or have some form of light “clamping” action on the water line some how, but only a true asshole would permanently attach them. Permanently attaching them requires extra effort/cost.