I doubt this is something that EA would want to happen, they make too much money by spraying their games all over every platform available.
Exactly, the money is in the software, not hardware. EA's business doesn't really stand to gain from such an arrangement, as it could cost them sales if they were made exclusive to one platform (although EA's shareholders might not care, depending on the premium a buyer would pay). Microsoft would benefit to a degree, as EA games exclusively on a Microsoft system would no doubt increase their marketshare. However, they would still have the huge initial outlay of cash/stock to make the acquisition happen, and they would know they wouldn't get all of EA's software sales because some of the consumers would stick with PlayStation and Nintendo anyway.
The only real endgame is to put pressure on Sony to do whatever it takes to keep EA, which would mean including Microsoft software on PlayStation, thus ending the hardware war (between MS and Sony, at least), since Microsoft would rather not be selling a box anyway.
(An unreal endgame would be forcing Sony out of the hardware business themselves, then licensing the "Xbox" platform to whatever electronics manufacturers that would like to take it on. The result is the same thing, Microsoft doesn't have to make the box.)