Practically all sailing vessels in use (some racing sailboats etc excepted) have auxiliary engines for moving in constricted areas like ports. Considering this accident happened with people up in the rigging, they were presumably hoisting or lowering the sails when the engine lost power and they drifted into the bridge.
I'd be surprised if any port would easily permit such a ship to come or go under sail power. Sailing a ship into port is risky at the best of times. Yachts may do it into a marina when the wind and tide are just right for fun it as a little bit of a flex. But ports have work to do and having out-of-control sailing ships three sheets to the wind, so to speak, having misjudged the tide or whatever, is just dangerous.
Also, having your ship stuck in port for days waiting for wind and tide to be suitable for leaving would have been commonplace before engines, as would bring becalmed for weeks on end and being unable to evade dangerous storms. None are probably high on the list of things these ships really want to be doing today.
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
I’ve heard (can’t tell for sure from the photos I’ve seen) that they were “dressing the yards” at the time - which is when the crew stands on top of the yards (the horizontal spars) side by side. It’s done for ceremonial or celebratory reasons, not for work.