Probably a number of reasons, number one being to prevent massive brakes being developed.
It does also have a number of advantages (for driver comfort anyway!!), like toe said to allow a bit of give in suspension. Designers i guess would make cars solid if they could as all ride characteristics/aero would be constant. However tyres are an undamped spring, so makes controlling them tricky...
Other possibilities are it reduces pressure/temperature sensitivity for a greater volume of gas. Or just down to the fact rubber/air is lightr than metal?? Reduction in undamped mass etc?