Why don’t motherboards have GPU and VRAM sockets?

Because a PCIe slot is more versatile, and for quite a few other reasons.

While one person might find a RX 6400 GPU optimal, with its 50 some watt TDP and 1080p medium capability, another person would rather have a 6500 XT integrated on the board, and another yet would want some monster GPU with several times that performance and TDP. If it were you, what model or performance tier should be integrated into the board?

Thirdly, quite a few boards, (AM4 and AM5 in particular), essentially come with much of the circuitry found in a video card---it is essentially a mobo+gpu combo assuming you drop in a processor with an iGPU (eg. 4700g, 5600g, 7700x, etc); these iGPU's are somewhat below the performance of the 6400 low end Radeon card (720p high to 1080p low performance tier).

As for size factor, there are quite a few low profile GPU models. For performance and wattage classes above what is found in these, manufacturers may need to go to liquid cooling, if they want to cater to this high performance+SFF crowd.

There are a variety of GPU configurations. Some use 100 W, some use 450 W; should all motherboards have 450 W VRMs? Memory bus widths vary from 128 bit to 512 bit. And socketed RAM cannot support ~20 GT/s signaling used by GDDR.

PC's are upgradeable, non-upgradeable pc's use integrated parts like a laptop, and are smaller.