Well with Heroes of the Storm they have 5 maps and each map has its own mode/features to it, yet nobody seems to mind that. Nor did anyone mid that when they held a tournament with a bunch of college teams.I personally stand by only having one game mode be the tournament mode but I would be fine with two max. Too many game modes makes for a wacky competitive setting and I don't think that's the best way to go.
My personal choice would be Splat Zones and then thegame mode that seems to be the second most competitive which is currently Turf War as it is the only other game mode currently released.
I think that if there ends up being more than like 6-7 modes that instead of having the modes preset like how you suggested earlier of game 1 will be mode a, game 2 mode b, etc. Teams should select the mode they want while picking the maps, like how I stated before how in the best of 5 Team A would pick map 1 and 3 but also pick the modes in which those maps are played on, and then team B picks the maps/modes for game 2 and 4.Hmmmmm I personally feel like having multiple game modes could only make the tournament setting more interesting especially after watching other competitive scenes. For now until we have those other gamemodes is hard to tell regardless what you say could easily happen in the long run, and I'm sure most people would be okay with that.