Doesn't need to be using PoW though.

It would improve the stock market by bringing transparency. Right now you've got transactions happening off market so as to not affect the price of stocks by creating a huge spike in demand and the only way you'll know something happened is by paying to have access to level 2 data or by trying to cross reference the big moves that need to be declared by major investors.

Not all blockchains need to me anonymous either, one used for that purpose could be centralized with users needing to be registered with the authority that has control over the chain.