Well, I would not know how to parse the mathematical formula `f g h x` without context and I would not have naturally read it as a function application. Function applications in math are usually written with parentheses and commas, except when explicitly using the lambda calculus notation or defining a specific syntax, which you don't have to do when using the usual syntax which you refer to as the one somebody encounters in high school, and which is also used in computer science and mathematics papers.
You are right on the fact that it's usual to define arbitrary operators in maths. It's also usual in math to use single letters, including Greek letters, for function names and constants or parameters, and this is fine in mathematical formulas or texts, when there are not too many of them and when there are explained next to the formula, but that would be a nightmare in a code base. Ever read a program written by a physicist, who translated their formula into a program, without having the "source"?
Weird operators are a feature when writing maths, but could be a code smell in a program. Unlike an academic paper, we have space, and we have auto-completion. Give me a proper, readable, easy to understand name, unless your operator is really omnipresent (it's a great thing we don't have to spell out +, ×, or - of course).
> It is not obvious that the kind of elementary algebraic notation one might encounter in high school is the best fit for programming which tends to deal with totally different things.
Indeed. What I am saying is that if you don't use this notation, it will probably feel less intuitive to many people because what they are used to is this algebraic notation we learn in high school. The Haskell notation might be more apt (and I definitely see its strengths).
However, the opposite is also true, so this is not really an argument: I have not found any real drawback to this notation after years of using it in my programs. This syntax do not feel verbose to me so the Haskell notation does not solve any problem I have.