Why does every radio station have a different carrier frequency?

That's not exactly true. Any frequency you choose has several radio stations on it,

but just not in the same city.

Frequency is what your radio uses to separate the individual stations. If two stations

in the same city transmitted on the same frequency, your radio couldn't separate them.

When you tuned to that frequency, you'd hear both of them at the same time, and you

couldn't understand either one.

Listen to the 27 MHz 'Citizen's Band' some time.