You need to either nurture newly born studios, buy them while they're young and relatively cheap due to not being famous or lure existing developers with big sums of money so they will develop exclusively for you.
Buying something like EA would probably mean an aggressive takeover, since they would reject being bought. And afterwards, the enormous money loss from not selling multiplatform games would nullify the purpose of buying such a big gun for exclusive games making. The value of that company would also decrease immensely.
I'm sure they could buy a few mid-size studios here and there. Bungie, From Software, Rocksteady, etc. But then they would need to convince players to buy their console for those exclusives games, which is hard if the following isn't large or enough of a fan. It can happen, but they would be bleeding money until it started being a profitable endeavour.
So, really. The solution is to nurture your own studios. But that takes patience, creativity and money over a long period of time. Hence why they bought their way into gaming, to set a quick foothold.
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