The problem with Earth in Mass Effect 3 is pretty simple in my mind;
The writers want us to care about Earth. Okay, sure.
They fail to make us care. Oh, crap.
We're supposed to care about Earth because... it's Earth. We like Earth, right? It's our home. It's our planet.
Except it's not. I care more about the Citadel than Earth in Mass Effect. Yeah, that's the key. "In Mass Effect".
Landing on Luna in Mass Effect 1 and looking up at Earth gave me a sense of awe and wonder, but we never really go to Earth. We don't know all that much about it. We don't connect to the people of Earth, to the locations, to the relevance it has...
To the players, Earth is just... Eh, something over there, who cares, SAVE THE HOT ASARI BABES INSTEAD!
We love the planet Earth, in real life. That does not translate to loving the planet Earth in Mass Effect, because it's not the same planet.
They really should have opened the game with Shepard's trial on Earth, walking around, talking to people, maybe have your first combat mission fighting off batarians who try to kill Shepard illegally because they don't believe the Hegemony will make the Alliance give Shepard up for execution.
Damn it, you can't just tell us (haha, get it? Tellus?) that we should care about Earth. You have to make us hurt when we see it burn.