Would a standardized graphics chip socket be sensible?
I think you're misunderstanding the situation a bit. There already is a specialized socket for GPUs -- that's what PCI Express x16 is! Like AGP before it, PCI Express is a fast bus designed to support communication between the CPU and GPU. (It also happens to be a PCI replacement, which is convenient for other peripherals.)

Integrated GPU/CPU combos target low-end and low-power systems. They're designed to be cheap and run cool. The nature of these systems is that their users fundamentally don't care about the GPU. It's just there to accelerate the graphics of the OS and maybe do some light gaming. Intel's GPUs were already on the low-performance end, so this was a good niche for them to target. AMD followed suit to compete in that space. If you care about GPU performance, you buy a discrete GPU.

So what does having a motherboard socket instead of a PCIx slot get you? Sharing system RAM is a very bad idea because high-end GPUs actually do need a ton of RAM. You'd need to cram another large heat sink/fan combo on the motherboard. And you'd end up basically reinventing PCI Express to communicate with the GPU.