The problem is not, as Lessig seems to believe, purely a question of the FCC's "DNA." It is the inevitable trade off of regulation v. non-regulation. Lessig, like many, generally wants a world with minimal rules except to prevent abuse of bottleneck market power. All well and good. So do I. But any government agency with the authority to regulate to prevent abuse is going to be subject to agency capture, to fail to act when needed, or act at the behest of incumbents when it should decline to act.
It is this problem which lies at the heart of the Libertarian/Free Market v. willingness to regulate dichotomy. David Friedman has probably made the point most honestly in arguing that while markets may create bad solutions, he thinks centralized problem solving in government will inevitably create worse solutions. I happen to think the evidence points the other way. Given the nature of profit maximizing firms, it is inevitable that lots of bad things are going to happen as a result of information asymmetry, collective action problems, and other factors that make reliance on unregulated markets problematic for achieving freedom of innovation, freedom of expression, or even maximizing wealth generation. So I go with a system that allows some public input and introduces some non-profit maximizing motives as being likely to produce less awful solutions.
What Lessig wants is not to eliminate the FCC. He just wants an FCC that works along the lines he would like. That calls for legislation to reform te FCC, not burning down the house.