Because the Supreme Court said so, thats why. No really, the constitutionality of DUI Checkpoints was challenged in a Michigan case called Michigan Dept. of State Police v. Sitz. Basically, the Supreme Court decided the infringement upon a driver who is stopped at a checkpoint is not as important as the Government's goal in stopping Drunk Drivers.
The Chief Justice in that case stated:
The Chief Justice in that case stated:
In sum, the balance of the State's interest in preventing drunken driving, the extent to which this system can reasonably be said to advance that interest, and the degree of intrusion upon individual motorists who are briefly stopped, weighs in favor of the state program. We therefore hold that it is consistent with the Fourth Amendment.