There is still much kvetching about character variety in tourneys (something about C. Storm and Thor, but I wasn’t really paying attention 
).
Why not step things up a notch from “random arbitrary low-powered version of a character must be part of your team” tourneys to full-on, “EVERY match, EVERY SINGLE character on your team is randomly picked for you” format??
To make this as interesting (and non-irritating) as possible, all characters should be at an equal baseline level of power (40?) with all skill levels trained up to, and locked at, 3. After you play a particular match, you immediately lose control of that team so you cannot upgrade any of those characters.
Obviously, this will seem very annoying to players who have spent tons of time and effort developing a certain team, and won’t reap the benefits of using that team. However, since characters don’t gain any actual experience or skills simply from playing matches (you would still win 70/140 ISO per match as normal), nothing is truly lost. You can still spend the ISO from your winnings to quietly level your main team in the background and still go at it in SHIELD PVP as normal.
To benefit D3P, this kind of tourney will let new players have a chance to take those pricey 3-star and 4-star cards for a spin and maybe get more interested in ponying up for some card packs. 
To benefit players, I think this kind of tourney would make playing really interesting and shake things up. It would also put a lot more emphasis on match-3 skill and strategy, IMO.