We always use the cruise line's excursions unless we know exactly what/where we want to go. If you miss the ship because of a private excursion then it's on you to get to the next port, and you're really screwed if it's not a US territory and you didn't bring your passport credit cards etc ashore with you.
On next week's cruise I'm taking my wife on an excursion to the 1st place I ever snorkelled way back in 1981. Christmas Cove off St Thomas.