I have slept aboard with The Moorings, as well as several smaller operators in BVI and St Thomas. Very little time to kill after provisioning/ storing provisions/unpacking/eating dinner nearby and then onto the boat and sleep! The main advantage o sleeping aboard is having completed these tasks the night before , boat ready(not a quick turn around, addable to depart earlier. Locking boat when gone and securing before sleep is common sense. I grew up in and era when most houses in neighborhood were unlocked 24/7. Not anymore.
I am sure crime occurs but stay close to marina, travel in groups, as in any travels.This is true whether sleeping aboard or staying in nearby hotel.

Regarding boats being swapped out if not available, this can happen (rarely) and ALL operators, big and small, will try everything possible short of giving you your money back. Moving you to identical boat is ideal for them. Upgrading to another boat in own fleet is possibility. Possible transferring to another operator. But ALL the operators want you to continue chartering. What separates operators (Hotal airline, yachts) is how they handle the situation to build customer loyalty. If situation occurs, likely to be dealing with owner of company in smaller operators.