Well there are examples out there of peoples starting out with not doing "Fan Art" per say.
Bobby Chiu (He started with train session by drawing peoples, that's how he became known)
Artgerm (He does Fan art, but not based on what is popular, based on companies he likes)
Jake Parker (He does Fan art as well, but again, not based on what "is popular", just to get views)
Piotr Jablonski (Never did Fan Art, and his name still got out there)
Ihor Pasternak (Never did Fan Art, he's doing his own Side Project and of course works in the industry)
Jakub Rozalski (Never did Fan art, but his work is getting seen especially his Side Project)
There is plenty of examples that the opposite is true. I am not advocating anything about not doing Fan Art, but I do think one has to draw a line if they are doing something "just for like" or simply because they genuinely like what a studio did, and decides to do a Fan Art of their work.
Just throwing in my thoughts, I am not as active when it comes to Art (since I am mainly focusing on Design) and do art more as a side but at a steady pace.
Overall this is something that continues to makes me ask myself, why? When I see the same suggestion, while the opposite also happens (peoples doing their own thing)
But who knows, maybe I am wrong, again just throwing out my own thoughts in regards to this whole Fan Art for Likes approach.
But yeah, not here to hate or disapprove any approach, rather just here to spark some thoughts for peoples to also consider, what kind of effect things do on a longer scale, is it something you like doing ,or is it simply for likes?