One thing that I have puzzled over is the oft-given advice that
output filters of TXs should be designed with a loaded Q of 10.

This suggests that 10 times the energy of a single cycle is being
stored in the circuit but that the energy of each cycle is passing
through to the antenna, so where does the extra energy come from
to store in the filter?

Oops! As so often happens when you explain things to people,
or phrase your question, it all becomes clear, so disregard this
enquiry!