But why can't you create a business that is an accredited investor, which invests in companies based on its LP's choices?

In other words: Let's say I want to invest $100 in SmallCompany.com, for the equivalent 100 shares. I make that bid, and if SmallCompany accepts the bid, then I give Me-VC.com (the accredited VC company) $100 and Me-VC would make an equivalent investment in SmallCompany of that amount, for that number of shares. If SmallCompany exits, I get a return commensurate with the number of shares Me-VC invested for me.

Edit: I developed a site to back this but I've been searching for someone to co-found on the business/legal side, which in this case, is by far the tougher role.