Honestly, as long as things like Silk Road exist there will always be a market for a completely anonymous currency if only as a means of transfer of funds.
All this would require is a service where you can borrow Bitcoins, right? Does a service like this not exist right now?
I guess the problem is that it's hard to enforce over the internet, when you lend Bitcoins to someone. What if they don't pay you back?
Bitcoin's anonymity will eventually collide with the trustworthiness needed to make something like what you've proposed work.