Powering while at anchor has always made me VERY nervous. A bit too much power and suddenly you're anchored by the stern with NO power, and the anchor rode attached to a very high chafe attachment point. That cruise ship was fortunate to have very accurate position information, and a propulsion system with the sensitivity to hold position.
My boat has quite a tendency to sail back and forth while anchored, which puts quite a strain on the anchor when at the extreme positions. I've managed to reduce this tendancy to nil by using a small steady sail. Added windage is insignificant, and it eliminates the beam-on conditions.