Here's the thing: you couldn't just make it 16:9 by extending the screen because, as you said, you'd have to crop the top and bottom. Which, to be honest, is pretty dumb. On the other hand, emulators for later consoles like the Dreamcast can play in 1920x1080 and expand the viewing window, which introduces artefacts like objects popping up, but you don't miss anything and it looks cool.
Going back to the NES and SNES, it wouldn't be difficult per se to remove stuff from the top and bottom, but why would you? Extending the playfield is great, but shrinking it is pointless. The only way to fix it is to do like Outrun Cannonball, which is a port of the original game with a new engine.
In a 3D game like Shenmue, you can extend the viewing area and see things that aren't normally in your immediate view, but you can't automatically do that on NES because... they don't exist. They'd need to be put into VRAM first. Actually, come to think of it, you COULD kind of extend the viewing area because the nametable has enough for two full screens. But more than likely the sprites will pop in on the edges, unless you modify the code to make them appear off screen.
What I'm saying is, theoretically, yes, you could make an emulator that could extend the NES screen, but the results would be very variable. But forget about doing it on real hardware.