Is that why they sell so many games, and have such a sizeable revenue, but still lose a crap load of money?

They have more than their fair share of million / multi-million sellers. And many of them franchise games that surely get cheaper every year to regurgitate out with incremental improvements over the previous release.

Should they drop all or some of those sports franchises and concentrate on the other parts of their gaming business which do make a decent profit?

Or are those sports franchises the only thing that's keeping EA from totally collapsing?

Or is something completely different responsible for their losses?

There's no way to know how much the licensing costs. I'm assuming the NBA and NHL licenses are cheaper because they aren't exclusive licenses, but it's just a guess.