Well, this would basically be like a mini-Battle Royale with a smaller prize, or LTS with 4 teams split into brackets instead of just 2 parties going at it. Another major difference is that players (I'm assuming) would be able to pick their own party members, like BR and unlike LTS.
I do like the idea of a bracket, the 2/3 (could make for some pretty hype stuff) and it being daily. I think it would be cool if there were small tournaments like this to get more players into PvP and stuff, but I could see a some trouble coming out of organizing it. For instance if there is more than enough players (for instance 21), some might be upset if they can't make it in, or if there's 19 and a full bracket can't be run.
If this was made like a mini-BR, that happened daily at a certain time but with a smaller prize, that would be cool. The bracket thing I'm not so sure would work, since some teams might get a free trip to finals, etc. But again I think for the most part this sounds just like Last Team Standing with [1v1]v[1v1] instead of 1v1. Personally I wouldn't mind if LTS was hosted instead of something like this (LTS seems like a lot less trouble to host than this might be), but I would also love if something like this was implemented. A small, daily tournament with brackets and perhaps a thread on the forums for the winners to reap some bragging rights could give players even more to look forward to and give more of a reason to be on.
tl;dr - I think something like this would be awesome, there's a lot of good directions the staff could go with this. But since it sounds a lot like another version of LTS then I wouldn't really mind if GMs don't start hosting something like this, since they can just host LTS.