I prefer detailed DMs with really deep campaign worlds that I can discover. I want those worlds to be built like a clock so that the interconnections are already there and are not waiting for me a player to invent them.
In the games that first overtly talked about "fail forward" techniques - eg Burning Wheel, HeroWars, etc - the player doesn't invent the world either. Control over backstory - and particularly over consequences of failure - is in the hands of the GM. But the backstory in "fail forward" games is not authored primarily in advance.
Having the backstory already authored, so that the players discover it like the workings of a clock, would be one example of the pre-authorship that "fail forward" as a technique is intended to avoid.
I would also add: worlds that are authored in response to player action declarations can also be very deep. If you look back at the actual play examples I have given above, I don't think they imply a "shallow" campaign world.
I want a game where the players as their characters confront challenges presented to them by the DM. They do everything in their power to achieve their goals
This is also true of the games I run. The GM authors the challenges. The players, via their PCs, confront them and do everything in their power to achieve those goals. Sometimes they succeed; sometimes they fail.
When they fail, new challenges result. (See some actual play examples upthread.)
For a good general discussion of this aspect of "fail forward" play, see the
Eero Tuovinen blog I've linked to already upthread.
In a "fail forward" game, however, the parameters of the challenges - ie what backstory is constraining the possibility of success - is not spelled out in advance. So the players can't, for instance, reduce the chance of failure to (near-)zero by exploiting the fiction. In this sort of play, the drama of confronting challenges is prioritised over the logistics of overcoming them. (Contrast Gygaxian D&D, which reverses those priorities.)
Those who want a consistent world
Who doesn't?
The idea that "fail forward" undermines consistency is another red herring. To go back to Mt Pudding, there is nothing inconsistent about a world in which climbers sometimes lose important gear down ravines.
One style actively involves the DM and players teaming at the metagame level to ensure that the story outcome is interesting and exciting. So players will happily throw their characters into trouble spots via some metagame construct even if the character would never want such a thing.
I agree with [MENTION=6696971]Manbearcat[/MENTION] that you are drawing a false dichotomy here.
I really think it would be helpful if you engaged with some of the actual play examples that have been posted upthread, Then you could talk about how actual games are actually being played rather than how you imagine them being played.
In my game where the PCs searched the ruined tower for the nickel-silver mace, and instead found black arrows apparently forged by the mage PC's brother
before his possession by a balrog, there was no "teaming at the metagame level". The players were just playing their PCs. What is different from the style that you seem to prefer is that I, the GM, authored some new campaign backstory as a result of the failed Scavenging check, so as to put the fiction into a situation which (i) was not what the PCs (and players) had wanted it to be, and (ii) forced the players to make new, hard choices.
That is "fail forward" in action.
The DM knows the capabilities of the party (and players).
That's not generally true for me as a GM, both in the sense that I don't memorise the players' character sheets - so they might have skills, equipment etc I don't know about or have forgotten about - and in the sense that I certainly can't extrapolate from everything on those sheets to every feasible action declaration the players might make for their PCs.
What I do know is the PCs' goals. (Which, in [MENTION=6698278]Emerikol[/MENTION]'s terms, have been "meta" authored by the players so as to lead to
action - a bit like Gygaxian D&D depending on the PCs being hungry for wealth and fame.) These are what I refer to in framing challenges. It's up to the players to work out what their PCs can, and want to, do in response to them. (In 4e I also know the PCs' levels. BW, though, doesn't have the same sort of scaling system that 4e has.)