Wrong. The Relays being destroyed does doom the galaxy.
Lets put it like this: how many fleets were at Earth if you did everything nearly perfectly? If you count the war assets you see, then the fleets include: All the Quarian fleets that can fight (a MASSIVE amount), at least four Human fleets, the Geth fleet (which is comparable in size of the Quarians), at least one Salarian fleet, Several Turian fleets, all the ground forces, and what's left of the Alliance ground forces. Not to mention the mercenaries you got from Aria...that's a LOT of people stuck in the Sol system.
Yes, you can use FTL drives to get back, but you'd need MASSIVE amounts of food and fuel for that journey. Is it possible? No, I don't think so, and this is why:
Now, the Sol system has one inhabitable planet: Earth. That's one planet that can sustain life and grow food. This planet was just utterly ravaged by the Reapers. Most likely their fuel and crops are down, food is scarce. There would probably be a food shortage for the humans, but now that they have to feed three times as many fleets? (not including the Geth, obviously) Sure, they can go to nearby systems...wait, those were ravaged by the Reapers, too.
Okay, fuel. They can just hop system to system, right?
Anyone else notice in the game that only CERTAIN systems had fuel depots? Not to mention Earth's fuel station probably got destroyed, and the machinery to create more probably got harvested by the Reapers.
Face it. The Galaxy is in a ****ty situation, even with the Reapers gone. By "saving" the galaxy, you've doomed hundreds, thousands, tens of thousands of people to die by starvation, vacuum if their ships run out of fuel mid-way to their destination...
But hey, the Reapers are gone, apparently. Maybe Bioware thought that was enough.