All ARM boards have on chip GFX that would not only need new drivers to be written, but are also often pretty closed and only supported via binary blobs under Linux. Once you go into more obscure solution allowing discrete GPUs you end up with much higher price tags.
Depending on the exact supported HW you could get a a barebones (board,CPU,RAM) for 150€ and a fraction of that for used HW.
Super cheap AMD laptops do exist, but support would of course be an issue (just like with any ARM laptop).
Getting that old AMD port into useable state seems feasible, while an ARM port would be a start from scratch with serious roadblocks to get to the same state.
