Not exactly. What did you loosen? Your goal is to bust out of the manacles, and I'm not sure that you've described making progress toward that goal. If you've "loosened" the manacles to the tune of reducing the DC by 1 on subsequent checks, but injured yourself to the point of Disadvantage on that check, then you're definitely not making progress.
Besides, being bound in manacles is normally a binary state. Breaking out is not something that the system typically measures in degrees.
If your realm of dragons and magic is mostly binary states, I suggest a game where the result are treated as such.
In mine, trying to break free, failing to do so but seeing them loosened noticeably at one of the joints, but needing to recover from the strain before trying again, shows a path that might take a few days to work them enough that that weakened joint will break or perhaps less if the character then focuses on anything that might help focus on that joint.
Thec5evsystem is not defined so that ability checks are binary pass fail but obviously allows any GM to choose to limit their world to that if they choose.
But, I think if one looks at some of the "d20 problems" folks often seem to cite with an eye to the fact that the core, base and foundation of the ability check is that a failed roll can be not just a binary failure but can be progress (not completion) with setbacks the that changes many of those dynamics to the good.
"Me too rolls" as in "we all search for loot" ... first time the GM says "great, everybody till tell me who failed" and then proceeds to describe minor find and problems for them followed by bigger finds but no problems for the others... that dynamic changes."As you looked thru that pile of crumpled debris, some of it shifted revealing some coins but crushing what looks to have been an artistically carved bell, now mostly flattened."
"We all look and listen for signs to see if the guy is lying" as they meet in a bar with questionable type... first time those who failed the roll find out later they are missing a pouch (cutpurse got close when they were especially focused on that guy's twitching during the part sbout... ) or that they did figure out he was lying but were wrong about what part he seemed lying about... dynamic changes.
Foraging... you did find some game and a little water... but what found you or what was that bush you brushed up agsinst that now seems to have caused that leg to swell by morning?
Sure, a GM is allowed to make all of these binaries, boring and then gripe about how repeated rolls and bounded accuracy blah blah blah on the jnternet... but the actual PHB system put at its core for ability checks that setback option right there up front and so the binary is not from the system.
Fail an attack roll or fail a save... obvious consequences due to the nature of the beast. There was no reason for there to need to be the third option (though optional success at cost rules in the DMG extends the setback into those of the GM chooses.)
But for ability checks the setback is part of its core and foundation.
But, hey, as everything the GM can choose to not use it and will see the impacts of that choice most clearly.