The idea is great, but I must point out the pitfalls as they are the things that would need resolution first.
1)Storage - where does it live, who keeps it/pays for storage or has it taking up space? What happens if this is lost?
2)Agreement on usage - who gets to use it, when, who gets priority if >1 person wants it at a certain time?
3)Do you have a "shareholder" strategy where you kinda own a %age of the car dependant on the parts and labour you invest?
4)What happens if someone stacks it/blows it up/etc?
I owned a 50/50 shared sprint car with one of my best mates, which worked well as we generally worked on it and used it together and shared costs. I can see it getting problematic with a wider group though.
I think the best approach would be to have one person "own" the car and everyone else rents it out, with maybe the club taking a small handshake, first come first served on rental bookings. The more time and stuff you put toward the car the less rental you pay. We could rent it via the shop, you provide transit...collect and return.
Still has many risks and flaws though.