Your 1st par highlights my point:  we don't know what we want to do in Syria, so what is it that the military is to achieve there?
Re the 3rd par:  while the military may have been the way "up/out" for some, in the time of war, it also serves as the place where young people get chewed up and spit out.  I believe that if we had children of the more well-to-do fighting in our armed forces, then the mental health services and all health follow-up services would be far, far better than they are.  Just because it has always been the children of poorer people who have served in the Armed Forces does not mean it need continue being like that.  We could effect a change if we chose to do so.   
I also think that it is disingenuous to be throwing the blame on "politicians" in general.  The fact is that the extreme wing of the Republican Party -- the Tea Party or the Freedom Caucus are the ones who have been the most obstructionist.  I don't think it's helpful to ignore that fact.