So, someone needs to start a total anonymous identityless exchange.
People can't even get their funds back from exchange owners whose identities are known. What makes you think that anyone who sets up a totally anonymous exchange is going to be trustworthy?
An anonymous echange alone wouldnt help. That would be worse than now because now we know the owner. A new exchange only can be without a central. P2P-like. The orderbook stored on all the nodes taking part and the transactions in a similar way like with bitcoins. If its created, open source and some guys who know code checked its safe i would trust that network way more than a new centralized stock exchange.