Note: I use the spelling "fanfiction" and it's what I'm used to.
"Fan fiction" does register more formally. If in fact "fan fiction" is common enough among fans already it might be prudent to choose it. If that's not the case and "fanfiction" is what the majority of fans themselves use (this is from what I can tell true), I don't think the fact that "fan fiction" is "dictionary and academia approved" is a good enough reason to encourage a change in spelling. I also can't imagine those reasons going over well with fandom at large at all.
I don't know if anyone else has experienced this, but "fan fiction" trips my eyes up. I'm used to using it, but in general "fanfiction" I think is more instantly identifiable when reading quickly.
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"Fan fiction" does register more formally. If in fact "fan fiction" is common enough among fans already it might be prudent to choose it. If that's not the case and "fanfiction" is what the majority of fans themselves use (this is from what I can tell true), I don't think the fact that "fan fiction" is "dictionary and academia approved" is a good enough reason to encourage a change in spelling. I also can't imagine those reasons going over well with fandom at large at all.
I don't know if anyone else has experienced this, but "fan fiction" trips my eyes up. I'm used to using it, but in general "fanfiction" I think is more instantly identifiable when reading quickly.