I would take a delay @ an alternate airport I could get to immediately any day than wondering for an hour or so I "might" be OK on one engine.  The passengers in all likelihood didn't realize there was a problem until the pilot informed them, but in case they did know; there would always be a few passengers worry out loud causing panic in the plane. Then there's the FAA who probably want to know why the pilot didn't land @ the first possible opportunity w/a plane load of passengers in the back. Remember  the outcry after the British Airways 747 shut down an engine after leaving LAX for London but continued on. Never hurts to put safety first & foremost in the Course of Action flowchart.  Plus, they got to see a part of Alaska most probably never would have seen & have a great story for the Grandchildren.