Given the politicians in charge when Greenspan finished his term — the Barney Frank crowd forcing lending institutions to finance bad-loan mortgages — it was obvious that Greenspan couldn’t do anything about it.
What you seem to have forgotten, is that Greenspan was Fed Chairman through Reagan, Bush I, Clinton, and Bush II — fantastic years for America’s economy.
Try reading Justin Martin’s book about Greenspan.
Greenspan made disastrous monetary errors in the 90’s and 2000’s that contributed mightily to where we are today. The fiscal/regulatory mistakes belonged to the politicians as you mention.