Penny brought up a good point about blowing the horn, and I guess it depends on the Captain. On the Majesty, I think he only blew the horn when we left Miami, and not anyplace else.
On my most recent cruise on the Enchantment, the captain came on again, about once a day, and blew the horn when leaving Port Everglades and Grand Cayman. I'm not sure about Cozumel, as I was at dinner on the ship when we left Cozumel.
Leaving Grand Cayman, there was some humor involving the activities director. The captain came over the PA system as the activities director was giving instructions on line dancing for the sail away party, which annoyed the activities director, and talking out loud, stated "Come on, Captain, not while I'm speaking." Then a few minutes later the captain blew the horn, to which the activities director responded, "Come on captain, behave yourself," because he was still explaining the instructions for line dancing.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)