Philosophically, sure, but how does that play out at the table in actual play, when my character has tried and failed to do something, and nothing concrete in the fiction is preventing my character from keeping at it? What prevents me as a player from simply declaring exactly the same action again?
Nothing. It’s just part of how we narrate the failure to do the thing.
Ok, but again, what if I don’t want to set a limit on how long I’m willing to spend? What if I say “as long as it takes”?
That sounds like a hypothetical with no actual use case to me, but I’ll run with it for a bit. In that case, the one roll becomes a determiner of how long it takes, either without a limit (assuming you succeed on saves to not fall asleep after enough time passes), or limited by the story or the other PCs.
The thing is, I want giving up to be my decision. Unless there’s something concrete in the fiction preventing me from keeping at it until I get it, I should have that option.
It is. You get to decide the details of the narration of the result of the check.
Seems arbitrary to me. Why can’t I try again as many times as I want? I know, I know, “you already did try again.” Well, unless something concrete in the fiction is stopping me, I want to try again again.
You already did. Full stop. That’s it. That’s the whole “philosophy”. Check made, results narrated, game moves on. If you want to come back to it after doing other actual stuff (taking 10 minutes to chill out and refocus is part of narrating the result of the check), go for it. Or come up with a
reason that this is a
different check, not just a reroll.
Eh, alright. Not my thing, personally.
It’s absolutely central to why I run the game the way I do in terms of retrying checks, so no surprise we don’t agree on this part.
No, D&D certainly doesn’t require binary checks. But usually it does employ binary checks, and the exceptions are usually just trinary or quarternary. It tends to be either pass/fail/fail by X or more, or pass by X or more/pass by less than X/fail by less than Y/fail by Y or more. And the more of these exceptions you make, the more you complicate an otherwise simple, elegant system. The binary nature of checks in D&D is, in my opinion, one of its greatest strengths. It keeps task resolution very streamlined and easy to use - and you can still make exceptions here and there where it makes sense to do so.
As for the swingyness, I think that’s a strength too. If I’m only calling for checks when success and failure are both realistic possibilities and failure has meaningful dramatic stakes, I want there to be a decent amount of swing. If that swing is undesirable, there’s a good chance it isn’t a task that should be resolved via a check.
I disagree with nearly all of that. This is actually where the root disconnect is, I think. I see binary results as the fall-back for when something isn’t important enough to make a scene out of.
Cool, looking forward to reading it!

This is really the biggest sticking point for me, so I’m going to try attacking it from a different angle. You say you stick to the agreed upon amount of time the player said they were willing to spend on the thing. Fair enough, I think people should stick to their agreements. But, is that agreement the only thing that’s keeping the character from trying for longer than the player said they would be willing to try for? If so, that’s a problem for me. That agreement has no fictional backing to it.
Okay. In my game, we figure out what you’re trying to do and how you’re trying to do it, what the stakes and consequences are, and then roll to see how the sequence of events plays out. We don’t generally go action by action, unless it feels like the scene needs that.
Taking out a guard, for instance, might be a stealth check, Athletics check, one attack roll, and another stealth or slight of hand to hide the body. We don’t roll initiative and play it out but by bit, because the scene doesn’t warrant that level of detail.
Yes, the player should uphold their end of the agreement, but speaking purely in terms of the fiction, the character should be able to change their mind, right? For that matter, why make the player decide that in advance? Why can’t the character try for a bit, see how it goes, and decide whether or not to continue based on how well they’re doing so far?
They can decide after the check if they want. And again, if they can establish a change in approach or circumstance, they
can try again.
Also, what reason might I as a player have to commit to one time frame or another? Do I get a bonus on the roll if I decide to spend enough time at it, or am I just wasting my character’s time if I decide to try for longer than the minimum amount of time required? If I get a bonus for spending longer, what are the limits of it? Can I take long enough that my bonus exceeds the DC?
Picking a time frame is there because we are rolling to resolve a
scene, not an action.
The other key thing here is, this stuff is all negotiable at my table. In my group, the DM does not rule over the table, they run the world engine and adjudicate. The group as a whole decides how that game engine works and what measures the DM uses to adjudicate.