That's a very important note there.
I didn't like parsers at first, but if people just gave it a chance, I'm sure many players would find even another fun part about this game.
Optimizing my DPS and beating my records have become a game within a game for me, and it makes content a lot more fun IMO. You don't have to be bad because you don't use parsers, but in most cases, you work harder to get those high numbers if you see how you're doing.
I compete with other players too, which makes it even more fun, and you also get a little better picture of what DPS you should be doing. You can't go 100% based on it, because the majority get below average DPS actually, but you can at least by decent at it, and then start improving even more.
When I say compete, I don't mean that I tell random people I've beat them on DPS or something... I leave all talk about DPS to FC and statics, but you can still compete with them without saying anything.
This leads me to one very important part if they were to introduce an in-game parser for yourself only... It has to somehow give you feedback on how well you're doing
The feedback would be mostly for casual players that don't want third-party parser, so it shouldn't tell them they are doing bad DPS if they don't hit those numbers hardcore progression players can get, but it should at least guide them to average DPS.