NADA saw the online shopping movement coming before it got here and was successfully able to lobby for legislation that did not allow online sales of new vehicles. All retail sales have to be completed through a dealership.

I wonder how Carvana got around this?

Since you can take your make-of-car to any dealership for warranty work or service (Service Depts and Parts Depts often are businesses within the dealership enterprise), this should not be an issue.

After buying the car, how often do we go back for concerns to the sales dept? Never?

Let's see how the dealers respond to this new business model.