As others have noted, I don't see how this differs from any other skit playing off of any other industry stereotype. I work in the private sector. Skits about the private sector revolve around how money-hungry it is and how we'll do anything to make a buck. Is that true of all of us? Of course not! But it's true of some - enough that a stereotype has been developed that we can laugh at.
As for the DMV, I've had mixed interactions. My first interaction in Minnesota was awful. Others since then haven't been so bad. One was good enough that I wrote a letter letting them know how good the customer service was.
The only way to really effect change with poor customer service is to speak up. If you have an exceptionally good or bad experience, report it. Unions or not, enough reports about someone do have an impact on one's employment.