If MS really wanted to become the Netflix of gaming, with availability on as many platforms as possible, then buying EA makes sense. They'd gain a lot of content, servers, subscribers to EA/Origin Access, and developers to make themselves a multi-platform leader in GaaS and subscription-based gaming over night.
I could imagine your Origin ID becoming an Xbox Live ID in the near term, boosting their MAU significantly, with the long-term prospect of getting users into Game Pass and eventually their streaming service.
I see several people think MS would want to make some games exclusive to Xbox and Windows, but I think it was Nadella who told Spencer to think beyond Windows, which is likely why Spencer no longer reports to the EVP of Windows. With that, I think everything would stay multi-platform, with Halo, Gears, Forza, etc going multi-platform eventually, perhaps way down the road when game streaming takes off and nobody gives a flip about the device it's running on, just as people feel about their movie and music streaming now.
Edit: As much sense as it makes given the direction of Xbox, it seems that MS could make better use of cash on more lucrative prospects on the business productivity side of things. Then again, maybe Nadella sees Xbox as Microsoft's best chance at staying relevant on the consumer side of things long term? Perhaps he thinks a big acquisition on the gaming side would make more money long term than letting all of that cash just sit there. Ultimaltely I doubt the EA acquisition has any chance, but I'm eager to see what other big whales they're looking at.