I get that you have a position and a conclusion you would like to support but the facts dont support you.Outside of your interpretation of "progress with setback", that very much describes the 5E ruleset. It's all about binary states. There's not even an example, anywhere, of them using anything like what you suggest. It's more like an afterthought, attached to the basic rules, for the purpose of governing unusual situations. There might be a situation, somewhere, where the logical consequence of narrowly failing a check is different than outright failure. If it was actually part of the core foundation of how ability checks were supposed to work, then you'd see almost every example incorporating that option.
That's not to say you're doing it wrong, of course; just that it doesn't necessarily follow. There's another way that the game can be played, which is more intuitive based on the wording in the book. The straightforward reading of the rules is that anyone with average Strength can break through DC 20 manacles within 2 minutes, because there's no real consequence for failure. That's not stopping any DM from instituting such a penalty for failure, but any penalty that you apply is going to reflect the nature of the DM rather than the ruleset itself.
There are THREE fundamental checks in the game- attack rolls, saves and ability checks.
Ability checks right there in their PHB direct tule on what the not meeting DC means establishes THREE outcomes... overcome, no progress, some progress and setback.
That's one of three establishing not an optional rule for three states but the base rule.
Attack rolls also by default have three states - fail (no damage), success (normal damage) and crit (extra damage),
So that takes two of the three core check types as baseline a non-binary result.
Saving throws are the one where it's more of a solid binary however even there you have a core example where non-binary is used - again core to the PHB - and that's Death Saves where a 1 and 20 produce different results than any other pass/fail save.
So, two of the three establish trinary results as the baseline core mechanic flat-out and the other establishes mostly binary but one of the core quite significant sub-sets uses trinary too - for something as vital as death.
Again, these are not hinting down some optional buried in the bowels of the DMG nuances or sage advice rulings... these are the base core definitions of how things work in 5e..
It may have been true in other editions that ability/skill was defined as binary pas/fail only but not 5e.
If a GM **chooses** to run his game as "binary" that choice and its results (including the 2 minute manacles 23 thing) are on them, not the system. The system does not limit that GM to that outcome by its core rule.
If you choose not to wear your seatbelts... not to use the alarm timer on your oven... not to lock your door...when bad things happen that those could have prevented is it a flaw of the makers of the car, stove and door?