Honestly, even EA themselves were still making interesting games back in that period. That was the era of stuff like Mirror's Edge, Dead Space, Syndicate, SSX, Alice, Spore; EA actually published video games back then. If they'd had the Star Wars licence back then we might have had some good stuff.
Instead, their getting the licence coincided with this move of theirs to the model of trying to establish microtransaction platforms instead of making video games, while publishing one or two indie games a year to maintain the illusion that they aren't all bad. They've chased profits so doggedly that they're now in this corner where the shareholders will revolt if they make anything other than sports games and shooters because that's where all the money is. And because you can't make a Star Wars soccer game, and apparently they can't make an open world game either, that only leaves Star Wars shooters.
Because if there's one thing I think of when I think of Star Wars, it's mindlessly shooting dozens upon dozens of people in the face!