Even with planets like Earth and Thessia being mostly wastelands, that doesn't mean it's going to be Mass Effect: Fallout Edition afterwards.
Billions of humans, turians, asari, quarians, etc. are still alive with their ships and knowledge of their technology. Not to say that it would be easy (dramatic resource shortages, conflict from desperation, etc.) and wouldn't take time, but it's not the end of the universe.
Look at how Germany looked back in 1945 after WWII and look at it now.
And even with the Mass Relays destroyed, I'm sure there are still planets within FTL travel distance of Earth that could be colonized by each race to suit their needs for survival. Of course, it would mean that until a substitute for the mass relays were discovered, the surviving fleets and troops on/around Earth would be permanently separated from their homeworlds and colonies throughout the galaxy (except for the Asari if they decide to travel back to Thessia and don't mind waiting upwards of hundreds of years to get there). It's tragic, but it beats being completely wiped out by the reapers.
I strongly believe that this is all a setup for how Mass Effect 4 (or perhaps a Mass Effect MMO) will continue the story. If they're going to continue the series, they have to have a largely consistent ending regardless of choices so they have that base to go from. Without it, they have to pick one ending, say "this is what actually happened", and invalidate the others, which would invalidate the whole concept of player choice anyways.
That said, I still hate the ending(s) and the direction they decided to take. Worse more than anything is just the ****** poor quality of them. They could have still went the same route and made them much better by including more cinematics and dialog, and thought the major plot hole points through more. An ending doesn't have to be sunshine and roses to be good, it just has to be done well.