Well my thoughts are that as fast as the game moves I'm not sure it would be very useful, like in Q3 Arena you have The Gauntlet and I don't see anybody using it really.
I could see some melee weapon used in a game mode like Minstagib where everybody just has the melee weapon, however they would have to be smaller maps because the game would take forever to get over with in mid to large size maps..
Maybe just a big square where everybody can see each other and start going at each other just with a melee weapon but I'm not sure it would catch on, I kinda liked the basketball mod for Nex, but that and other mods don't seem to stay popular more than a week or two.
And I fail to understand you when you say ..
The closest thing we have to a melee is the nex
A melee weapon is something that you use your hands with and usually swing, or just your fists and is only good when you are in close striking distance to the other person, the Nex is powerful and used at a great distance, a melee weapon is always the weakest and the one you start out in on most games as the default weapon, and the default weapon with unlimited ammo now is the laser, and if someone gets close enough to you and there was some sort of melee weapon all you have to do is laser jump to get away from them..how often does anybody stand close enough to a opponent long enough to hit them with something with such short range that a melee weapon would have?