Maybe not in the same league but if you want exotic looks but the reliability of a Honda, go NSX.
I've thought about this many times. You can find '91s for around $20k in very nice shape.
With kit cars, like Old's Cool said, the registration is a pain in the butt unless you find someone who has gone down that path. What is it? A Fiero or Lambo? Are all the emmissions components still on it? In cases of Shelby Cobra kit cars, depending on the state it might be registered as a '65 or you might have to call it a 2007 (if built in 2007) and thus have catalytic converters and pass emmissions.
Also getting parts can be a pain. Is the company that made the kit still in existence? (In the case of Ferrari kit cars, Enzo put an end to them so your lucky if you can find one buzzing around! Carroll Shelby almost did that with Cobras, although you can't call them that in his book!) Finding body parts in case of an accident may be difficult and finding someone to do the work may be tough.
Again, not raining on your parade but just some facts to consider.