Nail polish will flake too. You'd kinda have to sand the phone to get any sort of bite from a paint finish. If you want to go that route you'll want to get to close to automotive grade as you can. That means lots of sanding, keeping everything free of any finger grease and using a robust primer>color>clear coat combo.

A wrap will be easier 100% but if you want to go for it it's all about planning and prep