People can improve their play style without a parser. Is it useful to show someone that they can improve their rotation? Maybe. Do parser's lead to issues with harassment? Definitely. The fact is, a parser already exists as a third party system for PC. It doesn't need to exist on PS4. If it is such a great tool, SE would have added it in by now.
"Fun" is a flexible term. So, your definition of fun, will not mean the same thing as another person's definition of fun. For example, you find a parser to be "fun." I find a parser to be a life sucking tool on the game. It is all about opinion and past experience's or lack their of in other MMO's.