This would certainly benefit the Democrats, but I don't see it as a "solution". It would give states without large urban areas even less political leverage than they have now. Presidential campaigns would not even bother visiting most states, since locking up enough votes in large urban areas (all of which are solidly Democratic) would be sufficient to win the election all by itself.
The purpose of the Electoral College was to prevent a slim 51% majority of the country from running roughshod over the rest. It is serving that purpose.