The idea of a legacy implies a situation which has past, US hegemony continues to be a bull walk against against democracy and any idea of progressive movements in the middle east.
Where democracy has emerged as an indirect result of US intervention ie Afghanistan, it has been a post facto add on to what was originally and act of aggression by the US.
Chaz is correct in that the US has propped up and continues to prop up anti democratic regimes-currently Saudi Arabia, Bahrain to name just two where protest and democracy is ruthlessly suppressed. In fact the US position with favoured dictators is to support the dictator while he's playing ball (that means supplying the US with oil in this context), if the population try to seize power hold the line, and at a critical point at which the dictator is about to be overthrown switch sides to support the people.
Unfortunately for the US, UK and much of the West democracy in the middle east would be bad new for the US, opinion polls throughout the region consistently and overwhelmingly show opposition to the US role in the region, not surprising given the US's cynical approach.
Iran-the current focus of US and therefore western attention, is in no small part a US construct and expression of US hegemony.
The US/UK backed overthrowing of the tentative democracy in the 1950's, the installation and maintaining of a brutal, pro-western Shah, supplying intelligence and support for Iraq in it's war against Iran, and the current military pincer movement that sees US military forces surrounding Iran on all sides justifiably feed anti US opinion, and fuel religions extremism as a rallying point for anti US sentiment.
If Western domestic policy aspirations were matched in foreign policy decisions the world would be a very different place.
Even Ho-Chi-Minh who was educated in the US, inspired by the US anti-inperialist revolution hoped that the US would assist him in the overthrow of the French oppressors.
Had the US done so, then the they would have had much more influence in the eventual independence of Vietnam, than a failed war, millions of deaths and waste of resources. One can only imagine how much better the entire region would have been for millions of lives that were destroyed by the conflict and the destabilisation that enabled Pol Pot to take control in Cambodia.
As a consequence of that war children are to this day still suffering from UXB in Laos as the US dropped more ordinance on them than Germany received in WW2- even though the US did not even declare war on them!