I think Dipping should take a full action as coating a weapon in poison in 5e takes a full action. And it should have some kind of duration, even if that duration is 10 rounds. Otherwise I think it is mostly fine, maybe for immersions sake to light a metal weapon on fire it will need some kind of oil or fuel applied to the sword before hand? While arrows it should be relatively free and if you ignite a wooden staff or club that might be a bad idea and so the weapon can be damaged if you don't put out the fire? Might add function to mending if it is ever added.
The main issue is, there has to be some sort of penalty to offset a combat bonus, whether it be a bonus to hit or extra damage. It’s the same argument we are having with height and backstab.
The penalty usually was forgoing a turn to prepare, a specific class feature, or diminishing resources like spell slots. But dipping has no cost. There’s absolutely no reason (mathematically) not to dip when it offers free extra damage. Tactically you are weakening yourself by not dipping.
