[steventhedev]

I think this is partially because it's applicable to so many different domains (cryptography, statistics, etc) that each have their own notational quirks. Avoiding collisions between notation in the application domain is more important than preserving some "consistent" probability notation (similar to the examples given with dot products). But the issue isn't even limited to notation: Chebyshev has at least 9 valid ways to spell his name (more if you include non-latin alphabets).

The biggest issue I've encountered is borrowing lecture slides from different universities/lecturers and the notation changes between slides on the same topic (even small things like using square brackets instead of parentheses).