It was easy to fix ME3 in ME2 though....
You just had the council and the races heavily investing in securing the galaxy against the Reaper threat, IOW, taken the events of ME1 seriously. Then you would have Shepard investigating these awkward Collector events, while the wider galaxy was worried about the bigger picture and let you focus on these apparently smaller concerns.
This would have solved a lot of things in ME3. For starters, it would have given you a glimmer of hope in the beggining (you'd start thinking "hey, they came sooner than expected but we started to prepare for this ****"). You'd have a council despairing because they had no time to prepare for the slaughter, but there was sufficient R&D and war investment to make things more interesting: you could witness new tactics and new weaponry based on the Sovereign encounter. There would be a realistic edge that the game could play with: while the galaxy not being entirely ready, it wasn't a complete downer. The battle in Palaven would have been with a lot more tension (as it is right now, the pew pew is awesome to look at, but what is the point? No Reapers will fall under Turian fire, you know that and so there's zero tension), and some twists could be arranged (a general mood of hope increases until a really nasty blow is given to some big fleet at 2/3 of the game, destroying your hopes, then a final desperate plan is arranged to get you to the end of the game).
As it stands, it's a crescendo of hopelessness and whatever-we-are-doomed-anyway put on top of a frustrated scenario where your warnings were completely ignored and belittled, almost making you want to abandon the unworthy galaxy to its fate.