Plus, it's not clear what below water damage there might have been to rudder, prop, and hull from the "grounding experience in the surf.

It was abeam in sand and surf. Sometimes they use bridals hear for towing down in the Chesapeake when you have to pull it out of a sucked-in the mud grounding, or you have to tow the boat a ways. The tow guys don't want to risk the consequences of a snapped line any more than they want to damage the vessel more.

If the boat has no rudder, it also makes the boat more easily directed. (Unless you have some TransOceanic expert, like the ones around here, who can rig and control a rudderless vessel with a jury rig.)