While the checkpoint system is a pretty wise one because it's utilized in places that you can't turn around and if you see the lights you're either fine or you're screwed, that doesn't make a larger random test system sensible. I'm okay with checkpoints and I'm certainly okay with police testing somebody they pulled over under suspicion, but lets leave it at that.
Random sobriety tests are a waste of police resources and tax dollars. Forcing someone to take a sobriety test without probably cause is false imprisonment. The police can much better use their resources to stop drunk driving by observing behavior outside of sports arenas and bars, and make stops there. However, checkpoints often yield many drunk drivers as well as stolen property. Since these are not "random," they should continue.