Ask HN: Why don’t motherboards have GPU and VRAM sockets?
Especially as the cooling solutions are starting to take up 3 or more PCI slots, I question the packaging as an expansion card vs directly on mobo.
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.