It is interesting to see kids invent their own perfectly adequate, if peculiar, notation. In the first example with the quadrilaterals, the answers were all right. The math is not wrong, just written differently.
But this may not always be the case. For example, when they get to intervals and suddenly need to properly discriminate between intervals like (1,2], (1,2), [1,2) and [1,2].
I might ding that by just one point--if you use non-standard notation, you must properly define it. You won't always be dealing with cases where your idiosyncrasies have obvious answers and it's better to form good habits that allow you to communicate clearly with others. There may be many good ways to depart from convention and I'd hesitate to stop anyone from doing that, but I think that if defining your departure from convention is too burdensome to be worthwhile, then you do not have a compelling case to depart from it in the first place.
Society advances in two ways: in small incremental steps, and in large leaps. When we stick to existing notations and concepts we can make incremental improvements. But the large leaps often come from creating better notations and better conceptual understandings, which can turn substantial amounts of knowledge and logical thinking into obvious consequences of an organized and intuitive system.
Incidentally, in some contexts, (x,y) is how we write fractions (they are just an equivalence class based on an ordered pair of integers).
As long as I am on the subject, (x,y) also means the inner product of x and one. And I had one teacher for whom (x,y) means f(x,y) where f would change more or less every section based on convience.
On second thought, maybe we should be a little stricter in teaching students that math notation is rigid. If we raise a generation of mathematicians believing it, then they might clean up the current mess of notation we have today.