The symbols do have names, eg | is commonly called a ‘vertical bar’ or ‘pipe’. I think when people read the code though, they say the name of the operator instead, e.g. your example is ‘reverse max scan x’. A complication is that the meaning of a symbol depends on the surrounding symbols (eg | can be reverse or max) and another is that the meaning can depend on context, eg | is max but when the inputs are arrays of bits (where 1 is true and 0 is false), max is equivalent to logical or, and so people may call the operator ‘or’ in those contexts.

I think advocates would claim that the symbols allow for faster interaction with the computer and for larger programs to fit in one’s working memory.