As with any "common law" system, the start will have a lot of "pause moments". But it shouldn't last long. the first time you get a non-standard door, a pause is required. Maybe the next, or just the next really different case. Let's say you jointly agree that stuck doors need a Str check; DC from 5 for lightly jammed to 20 for "wood warped and expanded into the frame". Next stuck door, no pause should be needed - the GM has a pretty good set of precedent/ruling there to interpolate on. A few disparate types of "stuck" (rusted, wedged, etc.) later there should be enough "case law" to cover most doors that might be encountered without much dissent.
Another important angle, here, is the "sphere" of the decision. These are all setting elements; for an immersive game (as well as a gamist one) the GM gets authority over those anyway. they could choose a "barred with solid oaken beams on the far side door" if they chose to, so it's really not the same as a "house cats always do 2d10 damage with each claw that hits in this world" ruling.
One thing that helps in this kind of play is if the game includes a discussion of the probabilities and how those generally translate to fictional elements, and what that means. You necessarily need somewhat of a presumed playstyle to do this, because you want to reduce the probabilities down to a few rules of thumb (that work most of the time, but not all) without everyone having to understand every nuance of the math.
For example, in Burning Wheel, the baseline assumption on odds is that a mundane creature that is competent at a skill will have 4 dice (before any situational or other adjustments in the fiction), will get an average of 2 successes out of those dice, and thus has about a 50/50 shot at an "obstacle 2" (OB2) roll. That's somewhat on the gritty end, but only rolling when it really matters means that the character can bring resources to bear if he really wants it. So when a new BW GM goes to set an obstacle for a task, and the current examples don't exactly cut it, you can make those kind of determinations easily. A lot of stuff worth doing that is mundane is OB2, and if it is slightly easier or harder than that, it is OB1 or OB3 by definition. (Other BW books go into even more detail about how to apply this in more extreme circumstances.)
Now, I think those rules of thumb are a bit harder in a d20+mod vs DC system, because of the range of the die, and it being linear instead of a bell curve. That is, the basics of the math on probability are easier to understand, but the rules of thumb are a bit harder to state. And of course there is a wider range of playstyles expected than BW, too. So you end up needing different rules of thumb for different expectations. For one example (rough draft, probably has serious flaws in it):
More mythic than gritty, heroic type of actions with bias towards success, adventurers are generally compentent at being adventurers. Baseline is that success occurs roughly 2/3 of the time, all else being equal. Bad situations can pull this down temporarily, but concentrated use of character resources can push it up temporarily. A starting, competent creature is assumed to have a +6 to +8 in a skill. Therefore, the DC for mundane but important tasks is around 15. (Need an 8+ roll to hit 65% success. That roll, +7 on average from skill, hits the DC.)
Where it gets tricky in 3E/4E is deviating from those odds. It is so tempting to adjust the DC by increments of 5 up and down, but that doesn't leave much room for expectations. Really, those are pushing the limits, with 65% as your baseline assumption. 40% down to 90% up is practically sufficient range by itself (especially if you want to leave room for grittier variants with a different base line--such as 50% base, 25% to 75% adjustment). Developing such a game from scratch, I'd go with standard adjustment of 3 to the base, allow two such adjustments on each side of the baseline, and thus have a range of 35% most difficult to 95% most easy (remembering this is mythic side, with grit shifting the whole range down by about 15% to 20%).
So now can write guidelines as a competent character giving a task where results under pressure matters:
DC 9 - slim possiblity of failure, but otherwise routine
DC 12 - easier than normal
DC 15 - normal problem, will success more than fail
DC 18 - harder than normal, could go either way
DC 21 - can pull it off, but risky
These are the kinds of tasks that competent creatures often encounter, reduced down to five possible variations of difficulty. Any difficulty much below DC 9 is automatic success for any but an incompetent creature, and any difficulty above DC 21 is increasingly unreasonable for anyone not distinctly superior to starting competence.
Then, of course, in D&D you have to scale all of that for character advancement. Though note that there is no inherent reason why the skills have to advance every level, except that the wider range of DCs in 3E/4E come built in with that assumption. (+1 to one skil per level, with a "forced spreading" system is one way out of many.) With the above system, and judicious and slight scaling, you can top out the very worst typical DCs (i.e. high level but standard things) around DC 30. Leave odds worse than that to circumstances, even if predetermined in the situation. You end up with:
DC 24 - bad
DC 27 - really bad
DC 30 - you want me to do what!
If sneaking up on the dragon is a baseline of DC 24, that's bad enough. And then any situational or circumstance that makes it worse piles on top. The d20 remains relevant, the mods remain relevant, and I've got at most 8 variations on difficulty to remember, and the difficulties scale by 3 every time. (How bad is climbing this mountain? It's got snow and some tough overhangs, but nothing really nasty. Call it 2 up from the baseline, thus DC 21.)