Most of the "problems" with this are things that feel like they actually have some straigthforward fixes with some testing
If the problem is that characters are glass cannons, then simply upping the base HP and AC for all characters likely mitigates this problem if we're talking mechanics.
Alternatively, instead of "fight to the death" it's "damage race"- players don't die at 0, and it's a question of who does the MOST damage past lethal (so you need to hit them to dead, and THEN deal damage to make it count towards your total), this makes base hitpoints (and base hitpoint increases) work like "DR" versus scoring, as will healing (since it adds back to your hitpoints).
If initiative is such a huge problem, then why not get "rid" of it? Both players will slide on the same board before calculations (or one will slide and the other will cast, or both will cast- Basically both players announce all of their actions for the turn, then all of them are resolved at the same time). (this might only work for 1v1, though)
I would like to note that "PvP" doesn't always strictly mean that you are directly fighting another player.
I could easily see something like there is a room full of monsters (say, 11 boards), and you have two parties. You need to be the party who does the killing blow to take the "trophy" for that monster, whichever team gets to 6 trophies first wins (or just more if time is called first)- with extra bonuses for getting more than the minimum (go until time or all monsters killed). Maybe smaller parties than normal for this (4 people each instead of 10).
There should almost certainly be a way to do this which both allows high-end stuff (maybe not artifacts, I'd have to see- honestly I'd almost want to allow them just to see if I could beat them ;p), and still keeps game-balance relatively intact for the experience.