What if they are double mail mittens?
Hmm When do the first plate gauntlets appear?
Because modern combat amounts to every weapon being blunt force trauma, the reality is that maille is only partially protective. It will protect you from abrasions and things like that, but it will not protect against a whack with steel or rattan against delicate bones like your phalanges. What
is protecting those delicate bones is rigid defense. It's the rigidity that is dispersing impact force and preventing bones from bending in ways they shouldn't. Without those two things, your fingers will break. So, in order for maille to really protect your fingers, you'd have to have enough layers to make it rigid, which defeats the entire purpose of maille. It would also become so heavy at that point it would be doubly self-defeating because the mitten would become a weight on a long lever arm (in this case your actual arm) rendering the protection too unwieldy.
In the real middle ages, knights of the maille era were more worried about protecting their hands from cutting and slashing wounds that were incidental in combat. But if someone took a full on swing to their hand they new it was going to break or at least be pretty damaged. It was also the best they had for a long swath of time. Since we're more concerned with sport safety in what we do (we're not looking to kill, injure or maim people) maille is always a poor choice for hand protection. Even if hands are 'illegal targets' they just tend to get hit by accident too frequently to leave it to chance.