Yes, but it's an order of magnitude difference. Today a Falcon 9 launch cost ~$20 million, mostly because they throw away the second stage.

Propellant for a Falcon 9 launch is ~$500K.

Starship is more efficient than F9 but in terms of multiple launches per day, the supply chain is indeed a factor. An hourly launch cadence is going to consume roughly as much natural gas as Houston.