CS professors writes just as incomprehensible math as everyone else, as you can see many here brings up examples of CS professors writing incomprehensible math in their papers.
Math notations are two-dimensional and don't suffer very badly from structural ambiguities, so that actually fixes almost nothing.
The problem in unfamiliar math notations is rarely the chunking of which clump is a child of which clump.
E.g say that some paper uses, say, angle brackets, with some deep meaning that you can learn about if you recurse three levels down in the list of references.
I'm not confused that in <Ap>, the Ap thing is a child of the angle brackets; and calling it (frob (A p)) doesn't help much in this regard.
However, at least you can search literature for the word frob more easily than for angle brackets.
Also it's perhaps more likely to occur to the person using the frob notation that maybe they should define frob somwewhere.
CS as a field just seems to have a higher base standard for explaining their notation and ideas. It helps in cross-collaboration by making it significantly easier to self study.
Related to this, I'd say math books have a significantly worse pedagogical culture in regards to both notation and defining pre-requisites. It's very common for a math book to say "we expect readers to have taken a discrete math course" and not defining notation despite knowing the topics covered in discrete math vary greatly from school to school and may not overlap. Math professors frequently have to paper over these problems at Uni as they realize the class does not understand some notation. CS are just better about this, and I can only explain it as a part of the culture and tradition.