Nothing at all wrong with using grease. I can't think of a single reason why oil would be any better than grease for this application. The whole point is to avoid a dry galling of the aluminium socket of the crank arm against the steel of the BB axle. Any lube will do but grease stays in place a little better and provides more protection and is longer lasting for avoiding galvanic corrosion. It's all I've ever used on my BB axles and none of my bikes has suffered from any BB axle to crank arm woes of any sort.

No it won't. If the metal has been swaged out so it's all bell'ed out then tightening it harder won't do diddly. You're talking about cold pressure forming of the socket. "Broaching" is a cutting action. But poor terminology aside the socket is damaged from riding it loose so the ends are belled out and won't come back. If you force the arm on with excessive torque you will only end up with a small contact area in the center holding things in place. Not anywhere near enough to deal with the racking forces at work in a hard pedalled crank arm.