My mother and I picked up my 1968 coupe 43 years ago today. The car was built on June 3rd, three days ahead of schedule so, coincidentally, the build date on the door tag is also the day I took ownership. I remember everything very clearly from that day, most notably, seeing my car sitting on the dealership floor with the shop employees walking a picket line around it. They were very gracious and allowed us to take the car. However, the dealer had to put the plates on the car himself, and when he was finished they all applauded and he took a big bow. Then, the fun ride home! I didn't have my license yet, so I had to be a passenger on that first ride. It did allow me to check everything out. It also was the only time the passenger shoulder belt was used (the driver's side never has been). Once I discovered how uncomfortable it was, I stuck it back in place.
With regards to concours and showing a car, there were no tags on the battery, radiator, etc. The only things in the car were the paper sleeves on the sunvisors. We didn't even have the Autolite paper mats because the dealer threw in rubber mats before we left.