I think you're being hard on Greenspan here. For what it's worth, the Fed could have made matters even worse had it been run by someone else. I do think Greenspan saw himself as a Classical cowboy trying to rope in a wild horse. No one can really fix the problem of the Federal Reserve except Congress. I think Greenspan did his best to minimize the problem...and of course there are problems.
When we get right down to it, we don't look at Greenspan and say, "He was an awful Fed Chairmen!" We look at him and say, "The Feds got to go."
What could Greenspan have done about the fed as yet another Academic economist? Nothing. I honestly believe he protected our economy from more liberal Chairmen.
Greenspan jumped on a grenade for us. It didn't help us achieve the goal of removing the Fed, but I think he also held back inflation much more than his predicesor is going to.