Yeah, law firms in the U.S. are generally never venture backed, although lawyers in Silicon Valley involved with start-ups get paid a lot in stock options or get given stock in companies they do work for.

Most of the time its like Petercooper said, there are rules preventing ownership by non-lawyers. The idea being that a lawyer should not be controlled by a non-lawyer, because that person might pressure them to take actions that are not in the best interest of a client. Its not as much a privilege question (as tons of non-lawyers work in law firms) as much as it is a perceived problem of having a non-lawyer control the lawyer's paycheck (although that article does mention a public law firm would have disclosure requirements under the SEC which could conflict with attorney client privilege)..

For instance, in your example, a VC who controls a law firm will have vastly different goals than the lawyers, whose goals should be to advance the best interest of the clients.