A choke wants to took the current the same. (constant current) [not voltage]
A capacitor wants to keep voltage the same [not current]
The choke is big enough that current can not change much during one cycle of the RF.
It is true the the RF stays off the power supply in part because the choke blocks RF current from getting to the supply and there should be a capacitor from supply to ground that keeps the supply voltage constant.
The real purpose of the choke: If a resistor was used it will get hot. power loss The output voltage will be some where between ground and supply (max).
A choke wants to have 0 volts average across it. When the transistor is on, it makes half of the waveform from supply to ground. When the transistor is off it swings above supply by the same amount. So the output is from ground to 2x-supply. (max)