It would be great if it could be setup that way.
How i imagined its like 1 server with 1 - 4 dojos spaced out equally. Say the first dojo ended quickly, the game would save the replay for those frames but the tori's and dojo would remain as they are while the other fights continued in the other dojos. An IRL example I've always used to show this is a BJJ tournament (see picture) where there are multiple ongoing matches in the same space.
The benefits to this are pretty obvious but I'll still spell them out:
1. Knock out tournaments would play faster and look awesome as the number of dojos would go from 4 for the beginning fights, then 2 dojos for semifinals, and 1 dojo for the finals.
2. Clan servers would allow friends to play and talk simultaneously without having to wait in long queues.
3. Realistically this could only be applied to official mods like aikido/abd/wushi etc that have dojos that dont take up a lot of space.
matarika - wheter you think this is or isn't possible let me know if you think this is a cool idea
NAGA Tournament
It can be items that are given to the two players equally, and they decide strategically how to use it and when. Just bear in mind that I'm talking about particular type of servers here, and nothing that I think should be applied to the competitive scene.
I can imagine me using a power-up and appear behind my opponent then go "Omaua Mi Shenderiu" on them lmao... other than that I don't know what else might be effective and cool in battle.