Do you know a slide and grip hitch that has a loop ?
You mean, a "loop" which serves as a "handle" ( so, not an "eye", or a "nipping loop" ).
There are some ( symmetric or not ) climbing hitches where there are two ends coming out of the "nub", which then are joined together somehow, so the pull by the weight of the climber can be distributed on both ends. In particular, I can imagine that one can always join together the two ends of any "symmetric" climbing hitch, like the Prusik, or of the symmetric "grip" ( "tight" ) symmetric hitches, like
Rat Tail stopper, the
TackleClamp or the
Double Cow hitch, in order to get a "handle". This part of the hitch is not very important - if the "nub" of the hitch, the part that is in contact with the object, connects the wraps together and "locks" the ends, is already a good or a bad knot, any such "handle", with any additional "loop" or knot joining the two ends would be required, will not add or subtract anything regarding the initial good or bad quality of the knot.
" elegant": I did not know that any new knot should pass the 'decorative' category.
It is not the "
decorative" category, it is the "
beauty" category... Well, many knot tyers, even if they have many knotting years behind them, never manage to learn this - but I understand you are a newbie in this field, so you will have plenty of time and opportunities to learn it, and come to appreciate the value of symmetry ( which means an easy to be remembered and inspected knot ), of nice curves ( which means wide, gentle curvatures, so the tensile forces are distributed and dissipated by more segments within the knot s nub ), of few fully functional elements and none partially functioning or redundant ones ( which means economy of tying and untying time and material, and a smaller cross section and volume ), etc. First, we learn to make working tools. Then, we learn to make beautiful such tools - which are working even better ! Ford T and Ferrari, for example...
Any genius out there who can make ... and pass the tests above ?
You have misunderstood what a knot tyers does... He is not "a genius" or a rocket scientist

who creates something out of nothing - he is just one who happens to "meet" a good knot, while he is touring in KnotLand ! Knots are like very simple mathematical theorems, there are not man-made, they "exist", potentially, even if nobody has happened to notice how they could had been utilised.
It is the knot itself which is ingenious ! We do not make plans in advance, and long lists of criteria to be passed and of purposes to be fulfilled, and then tie / create out of nothing a particular knot that meets all those ! We just happen to find a simple enough knot ( which could had been found by anybody thousands of years ago, because it is just but one simple tangle of ropes, for KnotGod s sake ! ), out of the many that can be tied, which we can then utilize in a particular way - a way that was not "built in" the knot, the very moment Universe, and 3D space, and flexible materials were created !

See the Prusik : It is just a "doubled" / two pairs of wraps
Cow hitch, which, in its turn, is just a "doubled" / two wraps bight. The moment you have this Universe, you get the potentiality of the
Cow hitch and the Prusik, and the probability of some intelligent beings with fingers, who will form the shape of those knots with a piece of rope. However, the probability of some even more ( or much less...

) intelligent creatures, who will wish to climb on the peaks of steep, rocky mountains, just
because they are there, and they will wish to do this by using ropes, and not hot-ait balloons or helicopters, is even more minuscule...

. Prusik was one of those creatures, who happened to notice that he could utilize this particular simple tangle ( formed, without doubt, thousands of times before by thousands of people, while they were playing with ropes, since 40.000 BC... ), as a tool for this purpose. He did not MAKE this knot, he was not a cook who cooked a knot some client has ordered !

He used an "existing" knot as a tool for climbing, just as farmers in ancient Babylonia and Egypt used triangles and their geometrical properties as tools for measuring their fields. ( Notice that I place the "existing" between "question marks" - it will be a matter of endless debate, if a mathematical theorem or a knot is "discovered" or 'invented". However, even if they are "discovered", they are not discovered by any brave explorers, and if they are "invented", they are not invented by any geniuses ! It is not any more difficult to tie a knot, than doing
elementary arithmetic or geometry - it is just that people do not do this very often, perhaps because they do not really need knots any more, or because the "old" knots "do the job", so they do not find it worth the trouble to lose any more time to figure out new ones. So, no heros or geniuses of any kind or magnitude involved here, I am afraid...
I had "invented / discovered" (= met ) some knots, and I know ! )
Starting from a list of purposes and requirements, and trying to "built' a rope-made tool / object to satisfy them, is the wrong way to tie a knot. Starting from a simple tangle, and see if and how you can use it as a practical knot, is a much more productive way to proceed, IMHO.
I did many of those, but they did not pass the "Tests" above, they became more complicated than this one with more material, time to be tied and dressed.
Did you tied the
Double Cow hitch ? Are two
Cow hitches, the one next to the other, "
more complicated... with more material, time to be tied and dressed" ? I do not say that the
Double Cow hitch, is a "slide and grip" hitch, it is just a "grip" ( = tight" ) hitch, but it is very simple, in its form and its concept. You can also tie a
Double Prusik, which is an even tighter 8-wrap "grip" hitch.
I have watched how an ex-navy sailor ties a
Rat Tail Stopper. Believe me, he does it in seconds, and it is the simplest thing you can imagine !
I do not say that there is not any other hitch, or that there can be found no other hitch like those : I only say that your hitch looks too
artificially articulated to me...

If you had told me in the first place that my knot was that bad,
I did NOT tell you that your knot is THAT bad- or even that is bad ! I said that your knot is not as simple as I would had wished, it looks like it is still on the designing board, like a compound knotting mechanism which has not achieved the integrity of one coherent whole, the parts of which have not been fused together as much as in other rope-made mechanisms, etc... but I had NOT said that it is "
such a bad knot" !
ANY complex enough tangle of ropes will "do the job" and fulfil any long list of criteria - except the criterion it should be a simple, easy to remember, tie and untie knot, at about the same footing of already existing knots. See the Prussik : It is a "slide and grip" climbing hitch, which is perhaps / almost the simplest knot that can serve such a purpose. I am sure that, if Prusik himself had made a long list of requirements, he would nt had presented this knot, because it does not fulfil MANY of them : it does not smile, or serve hot coffee, for example...

However, it is a good knot...
I am sorry for having taken your analogy of pulleys as a real pulley system as
I thought of using the term "analogy", indeed, which is a word that I happen to understand very well ( I mean, through its etymology, history and evolution of its semantics ), but, at the end, I preferred "simpler", more "recent" words, like "representation" and "simulation". I had shown a simple
Cow hitch, and asked you to analyse it, and explain :
1. If there is any mechanical advantage in it ( there is, and I have tried to show where )
2. How one can analyse it, as a mechanical system ( I had drawn the directly "analogous"

simple mechanism, which does the same thing, if friction is considered to be negligible ).
I know that is is easy to analyse a simple machine : Those mechanisms have been invented and explained 2.300 years ago !

What I really want is to see how knots work as systems which are able to incorporate leverages and mechanical advantages - because they do ! When you tighten and "listen" a
TackleClamp hitch, you understand that there is a mechanical advantage somewhere, as the pole is squeezed much more that you could had squeezed it by your bare hands. However, to analyse and calculate the forces acting within it may be more difficult - and to explain this to another guy, as I had tried to do with my sketch in the case of the humble
Cow hitch, might be proved to be impossible !

I am not a good teacher, or, for that matter ( i.e., knots ), I am no teacher at all ! However, I believe that the knots I tie "
are not that bad", and I can understand if a knot I see is a good knot or not. Of course, we all have an opinion, especially about ourselves !
