With a fair amount of ambivalent results and reporting about the US military's effectiveness, an opportunity to push its rapid-response and logistical expertise to the limits was just what it needed.
And succeed it did. Despite major hangups at the Port-au-Prince airport and seaport, the US military successfully acted as the largest relief and charity organization in the country (and primary logistical/structural enabler for most of the other organizations there), and averted uncountable deaths during the disaster. Ultimately, the military's story is a story best told by those who were there. I recommend an article by Popular Mechanics written by a photographer/reporter in the thick of Haiti at the time.
Why's perception so important? If the US military can show it is in top rapid-response readiness and can muster highly effective logistical wizardry at a moment's notice, then it implicitly delivers the message that, despite the resource drain of Afghanistan and Iraq, despite alleged distractions, the US military still has the capability to organize and move huge amounts of equipment and manpower away from the US continent at a moment's notice--now is not the time to make a military move in the hopes that the US is too bogged down to respond. And ultimately, this display of power (if not force) acts as a deterrent to potentially disruptive smaller nations (like Venezuela) and, at the very least, causes bigger nations (like Russia or Iran) to think twice before considering a bold move.