For me, a fun car must be one that handles well. I cannot have fun in a Fiat 500 when I am worried of pushing its very low limits and crashing or losing control.
Regarding the potholes, I meant that its relatively high ride height makes it much better than a Mini or another lower car (most cars are lower unless you are talking SUV's). The bounces and rolls add to the, as you put it, 'fun' Italian experience!
I used to own a 2.5 ton Range Rover classic diesel many years ago. No roll anti bars fixed axels and definitely not fast but my god was it fun to drive around town the handling was awful but hilarious.
Pushing the limits of any car is fun, your argument about not having fun if the car isn't powerful might well be the same argument a supercar owner would make about any standard BMW or Audi