We only take independent excursions when the next port is nearby and getting there on our own would not be extremely expensive or difficult.
For example, if we miss the ship in the Caribbean and the next port is another nearby Caribbean island, or if we miss the ship in Juneau when the next port is Skagway or Icy Strait Point, that is quite different from missing the ship when the next port is half-way across the ocean.
But we have never missed a ship yet.
If you have any doubts, talk to your tour operator and ask what their backup plan is in case the vehicle or boat breaks down. We have found that most of them do have contingency plans in place.
Some of the boat and small plane operators promise that they will give you a free ride over to the next port if they don't get you back in time to catch your ship.
It is very common for the independent local tour operators to cooperate and have mutual agreements with each other to help each other out in such situations: You pick up my passengers if my vehicle/boat breaks down, and I'll do the same for you.
Since their livelihood and reputation depends on getting cruise ship passengers back to the pier on time, they are very conscientious about keeping track of each cruise ship's all-aboard time that day.