I'm not wholly opposed to HUDless games, but I think it only works properly in simulations, games that don't require the player to manage an inventory or resources, and games that don't rely on combat. If I'm playing a military simulator, I think manually keeping track of my ammo is a pretty reasonable expectation, but in a fast-paced arcade shooter, it really doesn't make much sense to deny that information to the player, since the game isn't about mimicing a real-life experience, but rather about creating a competitive environment to play in with a fixed and relatively easy to understand ruleset. Meanwhile, an adventure game could be either just fine without a HUD, or damaged by it - if it relies on self-contained challenges, or doesn't have any sort of inventory management, there's no problem, but when you start to add those systems a HUD becomes absolutely necessary.
It's also worth pointing out that in games, we lack three of our five most vital senses, touch most among them. We can't feel if our avatars have been injured, we have to rely on numbers and visual feedback like character animation to figure that out. HUD cues and interface sound effects exist largely because we simply can't know the state of the game in the same way we know the real world. Adding to that is the temporal factor. I can put down a game for days, weeks or even months before coming back to it, but what if I didn't have a HUD? I might know what items I have right now, but without some sort of record for the player to consult, it's impossible to just jump back into most games.
Ignoring the simulation component of games, of course, we've also got plenty of genres which are fundamentally abstractions. Chess is an abstraction of real-world warfare just as much as a strategy game like StarCraft is, and in those cases a HUD or at least some sort of easy-to-understand graphical representation of the world is necessary (in chess, it's the pieces and their positioning on the game board). These sorts of titles would be near-impossible without HUDs or HUD-like representations; it doesn't really count as HUDless for me if you still give all that information the same way, but put it on the character's gun instead of an out-of-universe status display.
As someone pointed out earlier, HUDs define RPGs because RPGs are defined by numbers. In a genre that's all about character skill instead of player skill, stats serve as a way to communicate the status of the world and the characters in it, and the game depends upon the player understanding that status, in order to make decisions based on it. As soon as you take those numbers away from the player, you don't have an RPG anymore - you have an action game. Imagine a racing sim where you can't see your speedometre... it makes the game more challenging, but does it make it more fun? Does it feel fair? No, because at that point you aren't making decisions based on solid information, you're playing a guessing game, and there's little challenge or reward in such things. Meanwhile, in Mario Kart there's no need for a way to check your speed, because you can so quickly and easily gauge it relative to the other racers, and there's really only two speeds for gameplay purposes, "fast" and "slow", and if you're slow, you're Doing It Wrong.
I've never been the biggest fan of trying to shoehorn the interface into the game world. I really hated Dead Space because it tried to make sense of all those necessary videogame abstractions, in a way that felt completely at odds with the realism of the world. Really? So they make mining suits that have health indicators on their backs? For who to see? Why? Some of the holographic stuff was fine with me, but harder to read than a conventional HUD. System Shock 2, Metroid Prime etc. do a much better job of it, and in those cases it didn't feel forced, but that's largely because they used traditional HUDs anyway, just modified for aesthetic "flavour" purposes.
As a gamer, I am more than willing to accept that games aren't VR simulators, and that we need HUDs. As a designer, I think a well-made HUD is necessary for most games, and it's better to roll with them than to try to force a design that requires a HUD into a HUDless space, not to mention that a well-made HUD can actually help enhance the feel of the world - we feel more connected to the worlds of Fallout, Planescape, Assassin's Creed, Half-Life, BioShock, etc. , not less, because the HUDs serve as believable portals into them. There is just no reason to get rid of them, and I don't see why we should try. It strikes me as just yet another gimmick.