If you don't mind your GameBoy being as fast as a supercomputer when it came out, then I think you could get an ARM SBC running a GameBoy emulator on Linux rendering into an OLED screen for less than $150 and a bit of your sanity.
If you're looking for hardware fidelity, I don't think it'd be in the "democratised" price range if you want to build a single unit that fits in a handheld form factor.
If you're looking for hardware fidelity, I don't think it'd be in the "democratised" price range if you want to build a single unit that fits in a handheld form factor.