I don't think I'm a particularly good player, but I'm a careful player because I'm a free player. I almost never die outside of danger rooms or later stages of arenas, and yet most players I meet manage to die at least once on every single floor. They die in the first fight of the first floor of a run, and immediately after healing at Basil. They die in spikes and brambles without any apparent lag. I'm ending more and more runs by myself because few players can make it past the first floors.
None of them seem to see a problem with this. They never notice that I'm not taking any damage from the enemies that are killing them repeatedly, or that I haven't dipped under half health for the entire run. Most of them will never get better at the game because they don't have any obvious encouragement to do so. They don't understand the effect of dying on their heat gains and their ability to finish a run.
I realize repeated revives are big money for OOO, but I think this has become a problem that is never going to solve itself. I can understand the need to swear off random groups for something more difficult, but... in Spiral Knights? Come on now.
There are a lot of ways to improve this situation, but generally speaking I think the best solution is give players who avoid taking damage and dying both positive and negative encouragement, and most importantly to make these changes very apparent to the player.
For positive encouragement, you could have enemies drop buff items that increase heat/crowns gained incrementally but are lost when the player takes damage. Show this with a distinct visual effect for drops, an alternate sound effect when heat/crowns are gained, a bar on the screen, etc. Give the player a cool visual effect that's visible to the entire group. You could go as far as to make the visuals stick around after the player returns to town, so they can show off. Suppose you actually gave each endgame armor set an awesome particle effect that only showed after a well-played run. This is the kind of dramatic encouragement that players need.
One negative encouragement would be to show very clearly how much heat a player has lost to deaths when heat is tallied at the end of a floor. Show it on the bar, with increments; this is the heat you lost with your first death, this is what you lost on the second, and so on.
While i think the play level tends to increase as you get "higher" into the game, and while i'm not 100% sure i agree with your premise... And while i think that there is incentive to play well (albeit no "extra incentive"), my eyes did light up when i read:
"uppose you actually gave each endgame armor set an awesome particle effect that only showed after a well-played run. This is the kind of dramatic encouragement that players need."
That would be fairly cool. And i can't argue that an incentive for solid play (a bigger incentive) wouldn't be unappreciated. Even if its something so simple as say a 1.10 multiplier added to your heat and money after you've completely finished the tier.
Also, it'd be kinda cool if that multiplier was a little greater for solo'ing a tier.