At least the last time that I looked into it, which was decades back, Virginia had serious limitations on using antique tags. I want to say you were limited to a few hundred miles per year, and the car could only be drive to, in or from shows, parades, etc. Things might have changed since then.
Back in the day, i.e. the same time period, car inspections in VA were a huge scam. The process was overseen by the state police, who would pull you over, tell you that they were going to give you a ticket for some bogus crap (I once had one tell me that I had to have a passenger side mirror even though the car never came with one), and then they'd "relent" and tell you that if you followed them to a repair shop and had the problem fixed immediately then you wouldn't get the ticket. The repair shop was in cahoots with the cop, and the cop would get a kickback from the very inflated cost of the "repair." Again, this is decades ago, and I haven't had this happen since I came back to VA in 2010, but when I was in high school it happened multiple times to me and many of my friends.