I'd argue it's a route through public airspace. If someone else wants to fly the same route, that's entirely their prerogative, similar to how everyone has the right to negotiate an off-ramp however they like.
If AK makes up their own approach, AK owns the piece of paper with the marks and letters on it describing the route. I would argue they don't own the route. If Delta independently creates a similar or same route, that's cool. If Delta steals AK's original piece of paper and simply copies the route, then Delta is guilty of stealing.
The goal is to come out of public airspace onto a public runway while not hitting things and maintaining legal or approved heights and distances. In some cases, to do that, especially in areas confined by granite, there will be only a few ways. This is public safety, efficiency, and public good were talking about