My mental state notwithstanding, I (and surely millions of others) have played plenty of sidescrollers using a joystick. Check out this little number if you think I'm full of shit:
But I guess there were no Mega Man games on the NES... oh wait, there were. Having played Castlevania: SOTN, Bionic Commando: Rearmed, Braid, and Sonic the Hedgehog using my Xbox 360 controller and its joystick, I find that it's pretty precise. Having said all that, yes, I am out of my mind.