I've read that
cars past a certain age cannot be imported under any circumstances, so that might be what precludes importing classic cars.
According to the link above, it's fine to import a used car if it is for personal use. I have friends who have acted as a sort of shill to import used cars before, so unless the rules have changed, importing something used shouldn't be a problem. But I'll have to look into it.
Have none of you been approached to use your FEC to import a car before? I used to be asked fairly regularly. Hasn't happened in the past year or so, but I've assumed that since I'm now a boring married person I'm just not hanging around the right types to be asked.