She knew the most about the Geth then anyone else and has fought them more than anyone else. She seems plenty qualified to be an admiral when they launch a war at the Geth. And it's not like she was leading ships like the other 4, but was more an adviser.
That is a horrible argument for making someone an Admiral. Especially when Tali's unique expertise of the Geth is an informed, rather than demonstrated, ability with no relevant need to promote her that high. Especially since Xen already has the Geth expertise/cyberwarfare weapon covered. Tali left the Flotilla about three years before her promotion, and spent, what, a year and a half with Shepard? Good thing the Alarai was wiped out, then, or else the Quarians must be pretty ignorant about their foe.
There's a word for the role of someone who is needed as an adviser but not power, and that word is adviser.
I mean, seriously Bioware. You're going to make a girl with less than three years of military experience and (as far as we know) two failed/doomed missions salvaged by outsiders a senior military commander? And then defend it by claiming you're just giving rank, not authority? I'm not sure if that's better or worse than claiming she was the best of the best after a rather lackluster justification in ME1.
If Tali seems plenty qualified, it's only because by comparison the Quarians are depicted as idiots. Thus making Tali, the fan favorite and companion, the only sane one in the room.