The simple fact is that a National rail extension to Newcastle Airport is going to be a wasteful duplication of existing resources. There is already through ticketing from NR to Metro and vice versa, which suits both worlds.
An example of a metro and NR serving an airport is Heathrow. But is this instance, the Piccadilly serves different stations from what Heathrow Connect and Heathrow express serve, but both are viable. The other factor to be considered is, crucially, how many passengers a month would use a train from Edinburgh to Newcastle airport?
As I say, whilst the journey is a bit longer, going to Central and changing to Metro is more cost effective for everyone.
Manchester will have both a National Rail and Metrolink service by 2016. However the Metrolink connection isn't really aimed at airport passengers but more at the airport workforce.