Tire sizes are a style element. After a while, the increasing size ends up affecting packaging too much and engineering will get the designers to start working the other way.
One of the smartest things Issigonis did when he designed the original Mini was put tiny tires on it. That left a lot more space in the interior and engine compartment. The small tires were also very inexpensive to replace, and to the surprise of many, didn't negatively impact handling. It's too bad everybody forgot those lessons.
Of course, large rims and tires are all about style. One of the reasons I drive an Acura is the cars doesn't have excessively wide or low profile tires. I find such tires tramline and have a harsh ride. I don't need 275-35-VR20 tires in my car. I will never need such traction as I do not race and wide tires aquaplane on Vancouver's wet roads.
I might add, Sir O, that Mini tires were infamous for how quickly they wore out.
