Home Servers need not be very small. If gaming is primary objective, you can add a 3060/70 or similar, or old gaming laptop, otherwise like you said current iGP

Home Servers need not be very small. If gaming is primary objective, you can add a 3060/70 or similar, or old gaming laptop, otherwise like you said current iGPU also serve purpose. OPs idea is to sacrifice CPU cores for iGPU, i.e. a home server with weak CPU but powerful iGPU, that is a small niche.