I've found that a lot of the younger generation that drive the sport compacts (Honda Civics with fart pipes, et al), tend to find the LBCs more fascinating than the Detroit Muscle Cars. The four cylinder engine is more familiar to them, and that they can actually tune one without the need for a computer intrigues them. Overall, the car is a lot more relatable to what they are driving currently. And, generally, an LBC is an easier car to get into financially than the 60's Detroit Muscle, as you can still find some decent deals on later Spridgets, particularly the rubber-bumpered Midgets.
There's always going to be someone who will appreciate a particular car -- how many people own Model Ts today that actually have childhood memories of them? Probably not many. What I'm seeing is a lot more interest in the '47 - '54 Detroit iron, not so much because people have childhood memories of them, but because you can still find decent examples priced reasonably for the hobbyists...and these cars are adaptable enough that you can pretty much go from a pure stock restoration to a completely insane custom.