My name may give away my opinion BUT if a bike, like my ~1955 Bianchi, is missing half of its paint that is the tipping point. Strip it down for a refinish. Since a freshly refinished frame looks terrible with rusty components I may as well go full tilt and make everything is shiny.
If a bike has a patina, not massive corrosion, all of the mechanical bits will get some loving which usually means lube/grease, new bearings, new cables, new tires/tubes, new chain and anything else that makes it safe and functional. If it is cosmetically challenged but structurally sound, I’m fine with that.
Finally, if there is stuff I think is in poor taste (i.e. Planet Bike fenders or camo bar wrap) I toss it.
My 2 cents…