Today I learned about the Jogcon controller for PS1 & PS2:
This was a dualshock where the analog sticks are replaced by a dial with force feedback, so players could play Ridge Racer and really FEEL the road as if the dial was a steering wheel. I have no clue if it was good (probably not), but I do miss a good weird controller.
Try a strategy title with the pads, in particular something like Civ, where there is no time limit. Right pad works fantastic as a mouse replacement. Left pad is always kind of just there, though it can be useful as a radial menu if you use the configurator (albeit that makes more sense on Steam Controller since the pads are round).