Because the US military has had to be more dynamic in its response to conflict since 1973 (Persian Gulf War, Iraq War, Afghanistan War), the All Volunteer Force concept has worked well, and was a marked improvement of the old model of drafting millions of Americans for short tours of involuntary duty.
Since 9/11, every American who volunteers for the military does so knowing full well they may be (in fact, likely will be) deployed to a combat theater. Our average soldier today tends to be a few years older than in the conscription army days, more well educated, and much more well trained. All of these attributes serve the US military well in terms of its combat effectiveness.
On the other hand, insurgencies typically last at least a decade, and this is the typical war we fight in the modern era. The Iraqi Army was defeated in three weeks, while the insurgency is still functional eight years after the invasion. In Afghanistan we have just passed the 10 year anniversary with very little observable progress in the strategic sense. So our AVF require asking for repeated year long deployments to combat zones, putting intense strain on military families, increasing the incidence of suicide and PTSD among front line troops, and creating very difficult adjustment periods for returning veterans. One could also argue that, with an AVF, it is easier for the government to wage wars that may or may not be wise because they do not have to justify a draft to the public or pass one through Congress.