As someone who takes his kids in an '80s pickup with no airbags, I support the idea. Plain and simple.
I do worry more about other drivers, but it's also not a FOREVER car. If weather isn't in our favor, I'll take one of our newer, safer, more comfortable vehicles.
If she is 21 and needs her one and only car to use on her own, a '64 C10 would be a terrible idea. As a 3rd or 4th car for your family, it makes much more sense.
Plus, the experiences she will have with you will last throughout her lifetime.