

If you remove the Luxemburg, Andorra, and a couple of smaller countries, VAT rates are relatively consistent. Indeed, if you live within 20km from the border, it’s worth buying some stuff across the border, and for some trips to plan a fuel stop on the right side of the border.
But if you need to drive 100 km, you won’t recover the cost of the road if you don’t do some specific purchases.
Note also, that at least in theory, you’re not free to travel with unlimited cigarettes and alcohol (where tax rates difference can be crazy) so again, if you pass by Luxemburg or Andorra, you can’t legally speaking buy 100 packs of cigarettes, (but would still save 30 to 50 € on a 10 packs carton)
Many countries have law banning stupid name which aren’t a way to give abusive power to a civil servant but to protect kids from crazy parents, so your example doesn’t work