A Southwest airliner recently had an issue where a "deflated tire indicator" showed on one of the landing gear tires after takeoff from Oakland, CA. They circled nearby for 4 hours while burning off fuel before landing back at Oakland.
In a circumstance like that, where there's no flight control or aerodynamic problem (i.e. landing gear door stuck open), why wouldn't the flight continue on to the destination airport and burn fuel along the way? The flight time is close to the amount of time they spent circling to burn off fuel, so it's not like they get on the ground any faster by staying near their source airport.
Note that this particular plane landed safely and inspection showed no indication of any real issue with the tire, but even if it did have a flat tire, would it be any worse to go on to the destination?
I suspect that it may be just in case another in-flight emergency forces the plane to divert to an alternate airport that may not have the full emergency equipment to deal with a landing gear problem, which raises the question: if the flight had departed from a small airport with limited emergency support, would the plane travel to an alternate airport with better emergency support?