Come to think of it what's stopping motherboard manufacturers from integrating graphics right into the motherboard? I always assumed this is what built on video actually was until I went AMD and found out the hard way. I guess is it a patent thing where they would not be allowed to because Intel, AMD and Nvidia own all the rights?
In the olden days processors used to communicate with memory via a separate chip on the motherboard (called the north bridge). Then you could easily just add an integrated GPU to the that chip (which had the memory controller anyway) and be done with it.
Once the memory controller was integrated to the CPU (ever since Athlon 64) this became much more complex. There were still some motherboards
that offered integrated GPU options, but these already had that GPU connected to system memory via PCIe, which is obviously less than ideal.
The alternative is to solder (GDDR) memory on to the motherboard directly for the GPU. On Laptops it's a common practice (and actually most mobile GPUs are built directly into the mobo) but on desktops the added cost of memory, GPU chip (and licencing) + more layers to the PCB make this a costly endeavor. These same MoBos have a PCIe slot anyway so it's much more natural to just have a separate budget GPU.
With the eve of Chiplets the CPU package is essentially becoming "the new motherboard" (when grossly simplifying things) e.g. the I/O die on AMDs chips is roughly the same as the old north bridge used to be. And according to leaks for instance AMD's Raphael (5nm Ryzen 7xxx series coming in 2022)
will presumably offer integrated GPUs as an optional chiplet.
TL;DR:
With current CPU architectures integrated GPUs that are not physically on the processor can't really use system memory well. Having to solder memory for the integrate GPU on the motherboard usually isn't worth it on the Desktop vs a discreet GPU.