The final list is a little surprising, these are all frisky old-school small cars that by modern standards are light and "tinny". So it seems that the fun-factor is the main reason, as distinct from the feel and general vibe of the car.
I have found with the 500 that it has extra character / personality, and the feeling that it gives something extra compared to all the other sanitised boring cars on the road today. There is a nice, solid, quality feel to the controls and fittings that sets it above e.g. the Panda and earlier Puntos etc.
For that reason I would include in the list the later Rover 200 / 25 model: my mum had from new an N-reg 1.4 8V that also had a quality feel with chunky steering wheel, firm seats and a lovely direct feeling when driving. The engine had a nice gruff growl and pulled well, and when I fitted 15" alloys the handling was surprisingly good. I always enjoyed borrowing it and experiencing the different feel compared to my Tipo and Brava.
The Rover was finally traded for a silver 500 Sport, but I was sad to see it go. It had a totally different front suspension setup to the Fiat design all our cars are stuck with, and never needed an endless stream of replacement wishbones, droplinks, ARB bushes etc.
A very underrated car IMO, the 16V engines are sadly notorious for HG failures, but the 8V was reliable if not terribly economical.