>But what if we could run the original binary game code unmodified, just with better art?

There's an entire category of rom hacks devoted to this - replacing just the sprite data.

You should also take a look at 3dSen. It’s an emulator that works with original NES ROMs but transforms the graphics into 3D voxels.

https://store.steampowered.com/app/1147940/3dSen_PC/