As a native speaker I would not use fan in the way you ask about, that is, with abstract qualities such as beauty, anger, intelligence. I could maybe use it with things such as popularity or sense of humor.
I'm a big fan of Elvis.
I'm a big fan of Elvis's hound dog.
I'm a big fan of Elvis's singing.
I'm a big fan of Elvis's guitar.
I'm a big fan of Elvis's pelvis.
I'm a big fan of Elvis's sense of humor.
I'm a big fan of Elvis's...
I guess they are not particular enough.
I have to turn to dictionaries, not because dictionaries determine usage but because they describe usage.
Oxford English Dictionary (OED):
A fanatic; in modern English (orig. U.S.): a keen and regular spectator of a (professional) sport, orig. of baseball; a regular supporter of a (professional) sports team; hence, a keen follower of a specified hobby or amusement, and gen. an enthusiast for a particular person or thing.
Merriam Webster Unabridged Dictionary:
1 an enthusiastic devotee of a sport (as baseball) or diversion (as ballet) usually as a spectator rather than a participant
an ardent admirer or champion (as of a person, technique, or pursuit) : enthusiast
Such things as sports, diversions, persons, techniques, pursuits seem more particular and much less abstract than qualities such as intelligence, beauty, popularity.
Where to draw the line between idiomatic and non-idiomatic usage? I cannot explain where or how...
Sense of humor can be seen as a technique. But popularity? Questionable. Intelligence, beauty, anger (even the Hulk's anger)...I could perhaps use admirer or detractor but not fan as in supporter, champion, or devotee. I can't put words to my usage, except say I would or I would not use this, ie I consider this or that to be idiomatic or not.