I've never really considered the comma as an "operator" but will do from now.

Neither did I for many years. Once you really understand how lists work in Perl (and why some people call the comma "the list operator"), then you understand enough about Perl's precedence and associativity that this sort of thing never trips you up much again.

Working through the exercises in the first chapter of Structure and Interpretation of Computer Programs (and working on a couple of parsers and compilers) cemented this knowledge for me. Fortunately, there's a shortcut: just remember that your computer prefers to do one thing at a time. Not everything can happen at once. There's a sequence to which operations happen.

Once you get that, you can reason your way to the need for associativity and precedence.