Y'all knew I had to jump in here at some point, didn't you?
About port time schedules. They have first to do with the local harbor authority and port costs (the harbor masters dictate the port times) and second to do with the rest of their schedule. It takes x hours at y speed to get from port to port and different ships have different speeds and can make different itineraries. That's why you often see the newer ships first in port in Cozumel - they're often a bit faster.
Ships excursions are designed for convenience of the passenger, and profit for the cruise line, not for best experience at the best price. For many cruisers, they're willing to pay for the convenience and security of a cruise excursion. Others (like me) avoid them whenever possible. There are a lot of resources out there for cruisers to work with reputable companies to get a superior experience usually at a lower price. Cruise Critic, for example, has Ports of Call boards and their Roll Call boards designed just for that.
You can have a great diving cruise. I often recommend it for my clients who are in "mixed" marriages - one partner dives, one doesn't. Several lines do a Cozumel, Grand Cayman, Roatan and Belize itinerary which is good, and some Eastern Caribbean itineraries are now visiting Grand Turk (usually along with at least one other diving port, on as short as a 5-night cruise), but my favorite itineraries for diving are in the Southern Caribbean. There are itineraries which go to ports like Bonaire, Curacao, Aruba, St. Lucia, Dominica, St. Thomas, Tortola, Barbados and others (of course not all on the same cruise). I've several times done 4-5 days of diving on a 7-night cruise. That is just a 2-tank day, and yes there isn't a lot of time left over afterwards, but it gets you a nice variety and keeps peace in the household.
Cruising isn't my preferred way to dive, as I like more time in a location. The only times I cruise the Caribbean anymore is for work, and this last time I didn't even take my gear (eeek!). But had I not just come back from a 2-week trip, and if I didn't have conflicting obligations (not to mention wanting a nice, long lunch with Christi), I'd have brought my gear and had no problem at all arranging dives. Takes a bit of effort, but it is worth it.