Power
You have the law on your side and you're not afraid to use it. Discriminating companies better watch out, because you're on the prowl. You know the rules like the back of your hand, and you're committed to upholding them.
While you don't get to make the laws, you do get to investigate wrongdoing and enforce those laws when the situation calls for it. Your power is especially powerful because you get to use it in service of the power-less.
People file complaints of discrimination with the EEOC because they feel they've been wronged by their employer, and perhaps because they feel they have nowhere else to turn. It's your job to stand up for the downtrodden, stick it to the corporate man, and score little victories for the little guys out there.
You get to walk into pretty much any company in the country and treat their executives like hapless interns. You need them to turn over documentation for your investigation? They're compelled to give you that info immediately. You want to talk face-to-face with the employer under investigation, or interview each of their employees individually? Sure, whatever you say. It's nice to have that power backed up by the Federal government.