I think you will find that at many airports "switchboard numbers" simply don't exist any more. There will always be a published airport number, but this will generally go either to an automated call gate, or to an information desk which won't necessarily have a facility for transferring calls elsewhere.

If you need to speak to an airline representative at an airport the person you will usually want will be the duty manager at the handling company (unless it's the airline's own base or one of their major hubs where they have their own staff). Numbers of duty managers don't tend to get published, and I suspect that if we were to somehow get hold of them and publish them here then they would soon change them. (I did once manage to persuade someone on a general airport number to give me the number of a handling agency duty manager... but it was on the basis of "You didn't get this from me, right?" and "Don't you dare pass this on to anyone")

So - nice idea, but I don't think we would get very far with it.