Swords are hardly useless against mail and gambeson, and I'm not sure where you're getting the idea from. The thing is, sword designs change depending on what the prominent armour of the day is, and looking at injuries can tell us just where exactly warriors struck.

With my area of study, armour heavier than leather or cloth is rare, and so swords are still incredibly effective weapons. That said, though, every warrior carried a spear, which basically nullified the protective capacities of mail - it's easier to punch through than cut, as you pointed out. However, that's not to say that mail makes you invulnerable. Riveted mail can still break due to stress put on it by a swinging sword, and we can see in the Gjermundbu shirt that it does have rents in it. Unfortunately, since Gjermundbu is the only verifiable shirt of mail from the era, we don't have much more to go on.

That said, though, we do have forensic evidence showing that mail would be broken and driven into wounds during battle, rather than being punched in by a spear, so there is evidence to show that swords or axes were effective weapons. Additionally, while they're not exactly fantastic sources, we have numerous accounts from sagas depicting brynjur being cut open by swords during battle.

Additionally, a large number of wounds on corpses, as well as literary references, indicate that the chest, upper arms, and thighs (which would be covered by armour) weren't the main targets of people with swords or axes, but rather lower limbs and the head were. This makes much more sense as they would be either lightly or completely unarmoured and let the attacker dispatch their opponent quickly and efficiently.