Sovereign tried. If I remember correctly it's been trying to send the signal to open the Citadel since the Rachni wars and is implied to have manipulated said war to try and make a play for the Citadel. The keepers locked it out because of Prothean meddling. The play with the geth was a more desperate plan. Could it have tried to bumrush the Citadel during peacetime? Maybe. But maybe the Council's response to a large unidentified warship of immense power suddenly appearing in the Widow Nebula is to immediately close the Citadel and call on the fleets to deal with it. A Reaper is not invincible. It needed to use subterfuge still. And the geth was the first army it could use that could challenge the Council races and without losing them to its own indoctrination.
Agree with the rest of your post, except Aria isn't a villain. 
Sovereign was awesome, definitely the best antagonist of the series. What Harbinger should've been. And miles above what the holokid ended up being.The thorian was also cool, something vastly different from anything else we've seen and a massively missed opportunity in ME3.Thorian > Leviathans. Saren also made a decent Dragon and is superior to subsequent humanoid villains. And I kinda miss Benezia too.
The Rachni wars were the Leviathans, trying to recruit a species to battle the Reapers. As far as I remember.
Sovereign had indoctrinated Saren and Benezia. Between the two of them they should have managed to sneak someone onto the Citadel and execute the relay procedure. Saren was a Spectre, he had all clearances and could have simply walked in while the Council wasn't in session. No one needed the Conduit at all, everyone involved had access to the front door, there was no need to find a back door. Neither would Sovereign have needed the Geth.
Even assuming that Sovereign needed to dock with the Citadel to accomplish its goals, it could have pretended to be an ancient prothean vessel which was found by Saren. Again, who's going to say no to the top Spectre if he wants to dock his ship so everyone's scientists can go aboard and study it? They would have welcomed him with open arms, because they were all eager to know more and were greedy for more new tech.
I am sure that there are several other ways to accomplish its goals without firing a single shot.
Sovereign fucked up badly on Eden Prime. First of all, it wasn't necessary to show itself, it could have sent Geth ships instead. Secondly, transforming the colonists and scientists into husks had no purpose and hinted at something else.
Saren's experiments with the Rachni queen and the Krogan clones made no sense either. What would those be used for? The Reapers didn't need them. Was Sovereign just humouring Saren? Was it a hobby?
Speaking of hobbies, what was up with Harbinger's little project? Collectors? Building a human Reaper? Why? What for?
Last but not least, the Reapers are a flawed creation and they do not make sense. Every Reaper is a gestalt AI which consists of millions of advanced, sentient programs. What do they need the genetic material of the dead races for? If the Reapers are storage devices for the history, culture, technology and knowledge of the races they wiped out, why would they risk themselves in combat? Doesn't that go against their directives of preserving organic life in Reaper form?
The Thorian was creepy and could have been more... except I kind of killed it in ME1. So there was no role for it to play in ME3. 
Aria is so a villain. She's a warlord, the ruler of Omega, the leader of all gang leaders. How is she not a villain? If you asked her, she'd tell you she is. 
P.S. I love Mass Effect but the writers didn't create good antagonists. The entire story only makes sense in hindsight, from the perspective of Commander Shepard. Just one example: On the first mission to Eden Prime you're accompanied by a Spectre named Nihlus who wants to evalute your skills because you are considered to become the first human Spectre. The problem is... Eden Prime was not planned to be a combat mission. If Sovereign and the Geth hadn't attacked, then the Normandy would have landed on a peaceful, agricultural planet, Shepard would have signed for the Prothean Beacon and then they would have flown to the Citadel. The only thing Nihlus could have judged would have been Shepard's prowess with paperwork.
And let's just forget about how the Council publically announces and broadcasts galaxywide the identity of their newest secret agent. Who becomes a celebrity that endorses stores on the Citadel. Yeah...