'Space-time is math model only; it does not exist as a physical reality'
Amrit, the math model cannot have a PHYSICAL STRUCTURE! For example a mathematical point cannot have a physical structure because it is a math model only. Since your essay affirms that 'According to loop quantum gravity, space itself consists of quanta' consequently space-time is a physical structure. Since space-time has a physical structure (quanta) then it is not a mathematical model but a real phenomenon. Therefore space-time really exist.
Thus your essay has the logical contradictions. You declare first that space-time do not exist. Then you agree that 'According to loop quantum gravity, space itself consists of quanta.' It contradicts one another.
Another error above: I'm surprised about your declaration that space-time and cosmic space are different things. The cosmic space is the same space-time!
'Idea of 'foam of space-time' is for me utterly wrong'
Spacetime foam is a concept in quantum mechanics, devised by John Wheeler in 1955 [Wikipedia]. On a small (Planck) scale, foamy bubbles result from the uncertainty principle, which allows virtual particles to spontaneously pop into and out of existence. Thus your essay and your timeless idea contradict to quantum mechanics. There are a lot of papers about foam of space-time published in the best mainstream Journals. There are indirect EXPERIMENTAL proofs that space-time foam really exist. (The Airy ring around the image of a distant quasar-like object).
'Physical time is run of clocks and run of clocks cannot be part of space' Run of clocks happens in space. So space is timeless. Idea of 'foam of space-time' is for me utterly wrong.
The concept 'Physical time is run of clocks' is erroneous because it is not the universal concept. There is no motion and clocks inside of a black hole. Therefore your concept is not universal and erroneous, because you cannot describe all time phenomena.
There is a logical error in your declaration above: 'Run of clocks happens in space. So space is timeless'. I do not see any logical way how to derive your timeless concept from the first proposition. In the same way I can write:
'Run of clocks happens in space. So space is a real phenomenon' Thus your theory is not a logical theory, but a collection of arbitrary hypotheses. I do not see any logical deduction and reasoning in your essay.
Besides there are logical contradictions in your essay: first you agree that 'According to loop quantum gravity, space itself consists of quanta' Then you write above: Idea of 'foam of space-time' is for me utterly wrong. The theory with contradictions cannot be true. Therefore your essay and your timeless idea is wrong.