I'm not a lawyer and therefore not qualified to expound on what "Three-pronged Test" or "Doctrine" decides what qualifies as an invasion of privacy, but...
If the cops could easily tell you were driving drunk, they'd pull you over and cuff you. They have no particular reason to suspect you're DUI if they have an armed checkpoint set up. There's the first problem, "no particular reason". That's not supposed to happen in America, that was what happened in Nazi Germany, and Soviet Russia.
The second problem comes from what's probably the real reason, or at least an important subsidiary reason, for the "DUI" armed checkpoints. According to some "N-Pronged Test" or "Doctrine" that non-lawyers can't possibly understand, the inside of your car is "public". If a cop sees something fishy, he or she can just search your car. That's the second problem: "DUI" checkpoints rapidly become fishing expeditions for whatever minor illegalities the cops can find.
The penalty structure for any crime or administrative infraction (at least in the USA) is set pretty high. This may have made sense when cops were few and far between. The USA had to make penalties pretty severe so that folks would stop at stop signs even when a cop wasn't there to watch. You didn't get caught very often, even if you did whatever crime. A fairly harsh punishment made sense in sparse cop circumstances.
But once you universally enforce some "sparse cop/harsh penalty" punishment regime, you've gone way off the ranch, and you're probably just doing it to increase revenue, either through fines, or through privatized prisons that need their bunks overfilled.
If the cops could easily tell you were driving drunk, they'd pull you over and cuff you. They have no particular reason to suspect you're DUI if they have an armed checkpoint set up. There's the first problem, "no particular reason". That's not supposed to happen in America, that was what happened in Nazi Germany, and Soviet Russia.
The second problem comes from what's probably the real reason, or at least an important subsidiary reason, for the "DUI" armed checkpoints. According to some "N-Pronged Test" or "Doctrine" that non-lawyers can't possibly understand, the inside of your car is "public". If a cop sees something fishy, he or she can just search your car. That's the second problem: "DUI" checkpoints rapidly become fishing expeditions for whatever minor illegalities the cops can find.
The penalty structure for any crime or administrative infraction (at least in the USA) is set pretty high. This may have made sense when cops were few and far between. The USA had to make penalties pretty severe so that folks would stop at stop signs even when a cop wasn't there to watch. You didn't get caught very often, even if you did whatever crime. A fairly harsh punishment made sense in sparse cop circumstances.
But once you universally enforce some "sparse cop/harsh penalty" punishment regime, you've gone way off the ranch, and you're probably just doing it to increase revenue, either through fines, or through privatized prisons that need their bunks overfilled.