I don't currently see any benefit in having stocks in a bitcoin like system. It's probably better to just have companies subcontract out their shareholder registry management to a company specialized in doing that sort of thing (exactly how they do now infact). Ultimately the investors are required to trust the company they invest in - if they don't there are a million ways things will go wrong and having the shareholder registry in a block chain won't stop that. With bitcoin as a currency there is now no single point of failure, with company stocks there is always a singe point of failure - the company. Having the company manage it's shareholder registry (or more likely subcontract it out to a register management firm) doesn't make any difference. If people want to invest in totally black companies that aren't registered with any government the same thing applies - the black company can still manage the shareholder registry with no additional risk. You're just trusting the management.. but you have no other option.
Quite the opposite.
Satoshi's key invention is that bitcoin is really a
distributed notary service.
Securely transferring stock from person A to person B is a perfect application for this invention.
As is securely transferring a DNS domain, or another digital entity.