The answer to your question, I believe, is with the Coast Guard and Amtrak's agreement about the number of trains that would operate on the shoreline.
There is a specified number of trains that were in an agreement relating to the bridges and the local maritime traffic. Amtrak when it scaled up for the Acela service, or when they wanted to add additional service entered into the agreement with CDOT to have people who have a SLE Monthly ride certain Amtrak trains for New London service.
This is brought out in the SLE Schedule and was discussed at one of the Connecticut Commuter Council meetings.