I see mounting to a stud as something useful if the outlet is expected to get a lot of use. The “wings” of old work box might possibly dig into the drywall and become loose. In this case the use level will be low, right? Besides, attaching to a stud is work intensive, and I believe that using an old work box like this is up to code. I’ve used them a number of times.
EDIT: Also about the caps… I try to observe a “code plus” approach and wrap caps with friction tape (NOT the plastic electrician’s tape). That stuff will provide a little more protection for decades.
Not the answer you’re looking for but we just put a cap over our double chimney. Our area has terrible pollution problems and, although we liked having fires, we’re happier not contributing to the area’s bad air.