What I loved most about my old Fiat Panda was that while it was small, it could easily go up over any pavement and with its 4wd drive it could handle even potholes and dirt roads with no danger.
Bigger wheels are generally a stupid idea from a performance standpoint. Smaller tires have better ride quality, cause less pothole damage, and are cheaper than larger ones. Big tires just look cool.
It necessarily does. Why are you even arguing this point? There's plenty of references that bigger wheels handle the same size obstruction (which includes potholes) much better.
Incorrect. They have advantages other than "looking cool"; shorter braking distance, more resilience to potholes, ruts and pebbles on the road, much better ride quality on imperfect roads, etc.