I think both Next itself and its defenders just don't get the significance of how the game does this. It really informs everything the game does, and you can't just arbitrarily change it and expect the rest of the game to keep on working as it did before.
I'm avoiding saying X, or Y, or Z is IMPOSSIBLE. I'm certainly sure that it is relatively simple in a basic sense to swap out one set of healing mechanics for another. It is at least difficult to see how A) the rest of the game can be tweaked easily to an adjusted healing system, and B) how the adventures can be useful in significantly different sorts of game.
In a sense the adventure question can just never be answered, but it does impose some limits on how much utility DDN has to whomever there aren't adventures written for. Still, I haven't found a D&D adventure pre-written that I was going to run in anything like its presented form in 20 years at least. That isn't true for everyone though.
[MENTION=85555]Bedrockgames[/MENTION], its hard to say how that would work without knowing what sort of assumptions there would be about hit points. In other words what do level 1 PCs start with? I'm not sure how you would get tension within an encounter. If I have enough hit points to burn on various heroic actions etc then at the start of the first encounter of the day I'd imagine my PC would be pretty loaded with hit points. It sounds like in general the PCs would have more hit points than the monsters do.
Consider how this works now in 4e, the PCs have LESS hit points than the monsters. They can access HS, which gives them a good bit higher daily total. Its pretty hard for a single PC in a given fight to access more than say 4 HS though, and that is digging far into their daily total unless they're something like a Cavalier or a Warden. The point is the PCs are more likely to reach critical hit point levels quickly than the monsters. Generally the party has to focus fire on monsters to dent them a lot, where even the lower damage output MM1 monsters can, in low heroic, easily bloody several PCs in a round, maybe even one per monster that hits with its encounter power.
If the PCs have say 4x the HP of the average monster, then in encounter one of the day they'll be in no danger at all, where the 4e PCs CAN certainly go down (and do often IME). Obviously HP will be a valuable resource and would dwindle as the day goes by and you'd be forced into management choices between using a 'hero point' and being able to keep taking damage, etc. The day would be more like one big 4e encounter though.
Frankly I think this is almost what Mike is thinking about when he talks about DDN adventures being "just built of a number of rounds" vs built up out of encounters. However DDN oddly lacks the key machinery, large hit point pools with HP used as a resource, or a hero point system that deflects blows, or something. In theory if you have a limiting resource like that and powers that (mostly) tap into that pool then you could do a fairly cinematic game, but it will feel VERY different from D&D. The PCs will start out plot armored to the gills and only towards the end of the 'day' (which could be one big encounter) will they start to feel worn down and really threatened. Most systems of this type also include some sort of 'body damage' or 'wound' type system to re-inject immediate threat (IE something that allows for the possibility of a lucky attack ganking a character right off or seriously debuffing them for a long time). Again, I feel like that sort of mechanic puts pacing back in the hands of the dice, and dice should IMHO never be in charge of anything unless the DM wants them to be.