I am sure that many of the practical knots we use today are derived AFTER they have been conceived as rope play or art, from the pre-historic times.
For instance, ...
I know that there is a - widely spread - popular misconception about human discoveries and inventions, their original causes, the motives that made our ancestors to discover/invent the tools we now use. In the case of knots, a naive reasoning might lead somebody to believe that there were first a need to tie something with a rope, and then a clever guy discovered/invented a knot to satisfy this need. A tool discovered/invented for some practical use. A plausible cause, but far from the truth nevertheless.
It is known that humans use tools to satisfy "higher", social needs, ( to help them been selected, and survive, within an antagonistic social group of other humans ), as well as "lower", personal ones ( to help them been selected, and survive, within a hostile physical environment ). The tools they have discovered/invented were beneficial not only to their evolution
as species, ( natural selection regarding the physical environment), but also to their evolution
within a species ( natural selection regarding the social environment).
(The same is true for many other animals as well. A well know case is the spectacular mating techniques of some birds )
A prehistoric human is wearing an animal fur. Has he invented this behaviour because he was feeling cold ? Or because he wishes to aquire the vital force of the dead animal ? Or because he wishes to persuade the male members of the group that he is the strongest one ? Or because he wishes to persuade the female members of the group that he is the fittest one ?
A prehistoric man is tying a knot. Has he invented this tool because he wishes to join two pieces of rope ? Or because he wishes to tie the hands and feet of his prisoner ? Or because he wishes to impress a female spectator ? Or because he wishes to pose a Gordian knot-type problem to his audience, that he, and he alone, can solve, as an able respectable magician ?
I believe that we underestimate the motives of inventions that stem out of higher mental functions of the human brain, and higher social functions of the human society. These functions helped our ancestors to survive within the social group, mate and reproduce more, cure their fear of death with religion, satisfy their curiosity with game, seduce their female partners with ornaments, deceive their enemies with disguised traps, gain the trust of their friends with reasonable arguments.
It seems too simple to me, that a prehistoric inventor first realized the practical need and usefulness of knots as rope structures that prevented slippage, and then invented them on purpose, to bind something, or to connect two short pieces of rope together. A scenario more akin to the true human nature, is one where this inventor try to elevate his own social status within a social group, with some kind of trick, game, ornament, beautiful piece of art, confusing mental problem or cunning deadly trap that will eliminate his adversaries. Humans are machines that manage to survive using clever tools, albeit for more complex tasks than we often tend to believe.