It might actually make money. Not much if any competition, and no alternatives (other than fly your own cessna). So fares can be higher than you might think.

However... while in industry history, it wasn't uncommon for feeder routes to operated at a loss to bring customers to the hub, that era is largely over.

If inter-island was being operated more as a loyalty thing, without much profit, that might be at risk. Most especially if AS finds itself losing money to carry pax to airports where they can jump on SW to the mainland...