We cruised with our son when he was a couple of weeks shy of his first birthday, so I can provide my perspective of the reasons. I had to care for him at home, so caring for him on the ship wasn't so difficult. But, it was made easier by not having to cook, clean (although we cleaned up after him), decide what to do in the evenings, etc. It was actually much easier to cruise with an almost-1-year-old than with the same child when he was almost 2 and almost 3. Not that it was bad, but at least he wasn't very mobile on that first cruise.
I wholeheartedly agree that kids should not be unaccompanied on ships. One of the reasons we eventually stopped sending our son to the kids programs (when he was around 10) was that they permitted the kids to go off on their own, and had activities where they'd be unsupervised. But that's a different situation than a baby. Most programs don't start until about age 3.