Can a sub-panel have a larger main breaker than the feeder breaker in the main panel?
You are fine.

The 200 amp breaker in the main panel will protect the wires leading to the sub. The main breaker in the sub is not strictly necessary, except as a local shutoff. You could as easily use a sub designed with no main, feeding directly to the bus bars.

The only requirement in this context is that the feeder breaker be sized to protect the feed wires and the sub panel itself.