I agree, in terms of fans, the cafe is massively overpowered. As a source of additional income, I'm not so sure. Unless you build one early(ish), by the time you can comfortable afford a cafe - you don't need additional income.
I could see the cafe (and theater?) as more of an early game thing. (The AKB048 model.) A step just past the "modeling agency" stage. (Though I'm not fond of that model, it is easiest starting strategy.)
OK I actually agree with both your points but wasn't sure if I was projecting: By the time you can get 10m to build a cafe, your concerts and singles make more than enough to offset any costs you have.
And I wasn't sure if I was crazy for feeling that the cafe is something we should get for free/cheap at the start of the game: it's already superior to the promotion and performance tasks by passively generating money and fans at the same time, just that it adds too many fans and kind of plays itself.