A/C Tripping breaker

Capacitors START the motor and the compressor. They are not needed/used once the compressor is running. IF the system is tripping the 30 amp also, that points to a defective compressor. The compressor starts and slowly the amp draw rises until it goes over 20 amps. You need to check the amp draw of the compressor as it is running, and monitor for 30 minutes. IF it is over 15 amps, it is defective.

Correct - they help start the motor. They are not being used after that but they are always in the circuit so if one were to short while the AC is running, it will stop everything.
The cap is not removed from the circuit once the motor starts, it just isn't necessary any more. It has to stay in the circuit to be charged again.

I don't understand these explanations. My RVP/Coleman air conditioner has a START capacitor and a RUN capacitor. I expect that all compressor-based air conditioners have the run capacitor and most have the start capacitor. The RVP wiring diagram for mine clearly shows that the start capacitor is removed from the circuit by the start relay, while the run capacitor is in the circuit all of the time. The service manual text also explicitly states this. I know from first-hand experience with other motor-driven devices that when the RUN capacitor fails the motor will draw more current and often pop a breaker. The purpose of the run capacitor is "to give the motors high starting torque and maintain high power factor during running" (quoted from RVP/Coleman service manual). Without the power factor correction the motor has to draw more current to pull its operating power from the power source.