Wax dip gives an added layer of protection and look great too.
The most functional part of a wax dip is to prevent crimp caps from rust from environment. Especially for beverages that will age in the bottle.
Wax doesn't prevent oxygen with caps, if the cap breaches the wax breaks too. If corking, then wax functions as the oxygen barrier.
Mtyh: Wax allows you to store beer on its side for aging. This is only true for corked bottles, to keep the cork wet and sealed. Wax on corked bottles allows vertical storage without o2 contact. Cap only bottles should never be stored on their side with or without wax.
Wax will prevent the lip crud from turning into something harmful. That little bit of beer that gets trapped in the outside crimps. Sometimes can't always be rinsed out. Wax seals it up.
In your case with swing tops. The sealing portion is glass and rubber so there's no rust issues. Imo wax in this case will give no benifiet other than cosmetic, and make for a mess to remove all the wax from the hinge for next use.