The Collectors hitting earth was conjecture on the side of the Shepard's teamamtes and no definative proof was offerd. Now admittedly, the Alliance functions better as a counter attcking force then as a defender, with flexibility being one of the key aspects of their stratgey, that being said the sheer fire power of the Alliance fleets would have been most likely be able to cut down the Collectors if they tried to rush through Arctutrus.
I do wonder were exactly it was mentioned that the Collector wiped out a turian patrol flottilla?
No, they're not. You've yet to provide any piece of definative evidence that confirms that assertion. Furthermore if the Alliance were so inept then the narrative would have to be able to proof that by itself without relying on conjecture, The list of succesfull military operations is merely an indication of why this clearly isn't the case.
In a game where character's words are essentially treated as truth, this was likely the case that Earth was in the Collector's sites. Something that also bothers me is how you're asking for 'proof' in the means of how a Young Earth Creationist demands proof for Evolution that is essentially in an unverifiable state. I can't be right, because you don't want me to be right. Strategy isn't really the big thing here; the issue is that the alliance has let it get as far as this to begin with. Or the Council.
TIM stated (and you can see the remains of the ship yourself on the mission) that the Turians were annihilated when they attacked the Collector ship.
As I stated, you're changing the use of proof to suit your purpose. The narrative does allow you to all out deny the usefulness of the alliance as it is. Shepard can repeatedly mention how he feels the alliance are blind idiots, Anderson acknowledges just how thick and stubborn the alliance really is, you have the entire Collector scenario of ME2 where the alliance chooses to essentially stick its head in the sand, you have the Reapers invasion and the alliance's stubborn refusal to listen or prepare, you have the Arrival situation (which falls into the last), you have plenty of characters outright mentioning that after Shepard died, the alliance just wanted to forget and hope the Reapers into non-existence.
A list of military victories, as I said, is unrelated to this. All that proves is that the alliance won military battles. If you're going to keep things connected via narrative, don't shift them to be connected by historical military engagements. You're essentially making your evidence fit your theory, rather than vice versa.