The port expects yachts to safely operate their vessels, and it's up to the captains to execute. That could mean sailing in / out of port, or it could mean under engine power.

The trouble I'm having is if they were leaving under engine power alone, with such fast current, why was the ground tackle not ready to be deployed?

We ran a much (much) smaller vessel with an unreliable engine and often pre-prepared our anchor before getting into port