You just hit the nail on the head. And Qualcomm could indeed do exactly this. All they would need to do is buy AMD. As they have over $22 billion in cash on hand, and AMD would probably cost them about $8-$10 billion to buy, they could do this and still have over $12 billion in cash on hand.
In return, Qualcomm would gain:
-an excellent Jim Keller-designed Zen x86 core CPU, about to be released, that was designed to scale from the largest datacentre CPU clusters to the smallest low-power x86 devices. Oh, and the only other x86 license currently available.
-a world class GPU core in the form of the Radeon Graphics divison, which would allow them to include additional advancements into their SnapDragon ARM chips, as well as break into the HPC GPU market place
-a footprint in the gaming world, which could be parlayed into better gaming chops for portable (either x86 or ARM) chips in Android phones, etc.
This, or an Apple buyout, for similar reasons, would make the most sense. A Microsoft buyout would essentially turn Microsoft into Apple, but with an x86 license to boot, and possibly a monopoly over gaming hardware for some time.
(bold italics mine)
Perhaps nVidia should merge with/buy out AMD. Then they'd have x86 as well as all the patents/technology from the Radeon division.