I think Plymouth and Newquay are different in a number of ways:
Plymouth is a small airport with limited runway length. It only has one operator, which was started by the company that owns the airport. It is a large city that has reasonable road and rail communications with the rest of the country.
Newquay is a larger airfield with a longer runway. It has a number of operators, albeit limited number of movements. It serves a remote area with scattered population, further from London, with no rail link.
Their relative proximity allowed a London service to be shared. Changes in fee levels at Gatwick no doubt played a part in the demise of the London link. I for one don't expect to see another operator at Plymouth until the economy improves, and perhaps not even then.
FlyBe has a decent hub at EXT which is only 40 miles from Plymouth, and Newquay will no doubt pull in some operators targeting holidaymakers. But with a sparse population with low propensity to travel, the far southwest will have difficulty attracting services from other carriers.