It's not really the case normal metal transmission lines don't have some "extra" L, is it? The magnetic field still penetrates into any real metal, so you have

It's not really the case normal metal transmission lines don't have some "extra" L, is it? The magnetic field still penetrates into any real metal, so you have some extra inductance. But I agree that it's very important to understand that a superconductor is not the same thing as a "perfect conductor", and the kinetic inductance is a great example of this. The ideas behind MKIDs are very cool.