I voted no.
War is a great way to show off the strengths of given elements and their powerful and interesting combinations--sometimes built by plan, other times by necessity. You can play against decks where you have some imperfect information about them (50% card type) but no perfect idea about how to counter. This is a great event to coordinate with other players on your team to come up with creative decks for match that offers knowns and unknowns without being totally random.
A Team Rainbow, on the other hand, would be a totally different exercise. Since they'd be required to play some sort of rainbow deck, they would not show the strengths of any given element per se. Further, in the theme of War, who exactly are they fighting for or fighting against? I also fear there would be a lot of redundancy in the decks that we see already--while I'm no expert or deck visionary, I'd predict a lot of nova/Snova, quantum pillars, quinted growth creatures, or speedbows. If I wanted to play against those, there's always T50 and PvP.
On a separate note, we'd see fewer discords (maybe a good thing) and possibly more BH.