EA don't make games, they publish them. Other companies make the game and EA ruin it with their money grabbing antics, but I digress. For example, The Sims was created by Maxxis, the Battlefield series was created by Dice, not EA.
I would imagine that the idea has probably already been turned into a game, but there's always room for another in the market.
The only companies that would be interested in something would be a small independent company, big companies have their own teams of writers already. Try a Google search for independent game companies and see what you get and go from there. You'd want to contact their game development team with your ideas when you find a suitable company.