Mass Effect FTL is limited in range and slow (from Ashley's dialogue in the first game it's around 12ly/day, which means it would take about 30 years for the Quarians to get home. Or at least it would if the Reapers hadn't destroyed pretty much every fuel depot in the galaxy and there was anywhere for them to get fuel).
I'm not quite sure where the 'everybody being stuck in Sol' bit is coming from. In the game itself you seem to zip around between regions using Mass Relays but you happily travel to nearby systems without using them meaning that getting home is a long haul, but possible. The Mass Relays taking out the entire solar system they are in is rather more of a pressing issue...one that wouldn't exist without that crappy Arrival DLC.