AFAIK, every edition of d&d has listed rope prices in 50 foot increments... As such it should be impossible to have less than 50 feet if rope unless the rope has been damaged or is also being used to restrain other individuals. That right there clears away the TV/movie scenario of several inches of rope tied around the wrists to be slipped out of unless some additional thing is done and that's critically important. There is no problem created if Bob can't untie himself because Alice can untie Bob and Bob can untie Cindy.
I really don't understand what you are trying to say here.
Anyway, back to the original topic, I feel like a lot of folks in this thread have conflated breaking out of ropes with breaking out of chains or manacles. Getting out of metal restraints uses a Strength skill to break or a Dexterity skill to escape. Which makes sense because you have to physically distort the metal in some way (very hard) or bend yourself in very odd ways to get out of stiff restraints.
But one of the key differences about rope is that it's much more malleable. It stretches. It bends. It both slides along itself and has friction with itself. One of the reasons I propose using an Athletics check for breaking free from rope is that you don't have to break the rope to escape, you just need to make one or two of the loops a little bigger, slide a knot a little bit, or stretch the material just enough. Even if a knot is tied perfectly, you might still be able to force your way out without ever breaking the rope.
Of course, plastic materials (like zip ties) would be a third thing, altogether.