I think that's a great idea.
For woodworking, for instance, woodworking clubs exists where one can
use the tools and shop.
Here in CT we have a maritime museum where one can actually build your
own dory with guidance. Clearly, stuff like this exists and can be
done.

One of the harder issues to deal with would be to make it a safe
environment, as one wouldn't want anyone to get hurt.
Also, you would have to have knowledgeable personnel there, both for
safety and obviously guidance. That could be harder, people that
actually know cars and are good teachers are not really dime a dozen.
Good luck with it.
Remco