The title pretty much says it
This mode is very fun, it's a breath of fresh air when you get tired of TDM and the like and it's sure as hell innovative!
No it would be as dead as Co-op hunter in less than a month it doesn't have much playability and would get boring easily. The reason it's so popular is because it's fresh adding it permanently would make it stale.
Would work if they added it in a best of the lab playlist. Obviously replacing the lab playlist.
As much fun as dodgeball is, I would not set it up as a single mode. Rather I would have a Lab mode, where you ONLY play on block mesh maps, and with random LAB modes only (one of them the dodgeball map).
It would provide a high variability on modes and maps, and since it is randomly you need to kinda manage your loadouts like that you can play each variant somehow (so you switch more there too).
Since there are now a lot of mesh maps and a lot of lab modes we were able to play, this mode would probably never ever get boring.