This concept sounds like a lot of fun for experimenting with different builds etc. I'd love to play it (for one day, until frustration makes me ragequit, but that's only due to my personal lack of roguelike skill), but there would be a few problems.
Provided that players increase in power at similar rates mostly proportional to dungeon progress, there'd be an average chance of about 50% of dying in every battle, which means that your odds of making significant progress would be incredibly slim (you'd only survive the tenth battle in one in every 1024 runs), which makes for a very frustrating experience, and the whole game would feel kinda futile. (Look at a mostly unrelated, innovative but unfun game called
Bokosuka Wars to see what I'm talking about)
If defeating other players early on gave you such a big advantage that there could be great differences between players on the same dungeon level, on the other hand, the especially lucky or cunning players would just mow down their opponents like mobs in a usual rogulike (kinda like a more extreme version of when someone's fed in a MOBA game).
And after a while, an "elite" of players would appear, and from that point on, it'd likely have a horrid learning curve and a very static metagame, where a few copy-paste builds with slight variations dominate everything and there's no room for experimentation anymore.
The best way to deal with these problems would probably be a system where your power scales noticeably, but not too extremely with items found and enemies slain, so weaker characters would have to avoid confronting stronger ones directly in order to survive, but had a chance to even the odds via traps and manipulation of the environment. This would fit a fairly cooperative approach where forming temporary alliances and engaging in combat as a group would play a big role... but the trolling and backstabbing involved could cause an unpleasant amount of drama.
Permadeath, long games and PvP don't combine well imo. As I said, I'd at the very least enjoy the concept, mechanics and atmosphere of such a game though...
Speaking of dungeon crawlers, the demo of
The Drop is already quite fun, and the concept of the complete game seems very promising. It's a spiritual successor to
The Reconstruction and
I Miss The Sunrise (aka "these laggy pretentious RPGs with the weird health system"), and puts emphasis on studying item and enemy properties and manipulating the environment.