Well thats also a very nice concept. Would be really motivating to get better and better over the time.
I think the best would be 2 modes. A sandbox mode where you can overlevel and overequip your character as much as it gets to just play around with friends.
And then a serious mode like the one you've mentioned. With actual matchmaking, rankings and a progress.
There are tons of potential.
The arena mode as of today was the only disapointment of this wonderful game for me.
