Again, because you are uneducated, and are attempting to read a document geared at legal practitioners, you do not understand the nature of the terms you are reading. This is not your fault; unless you've been to law school or something similar, you are not going to understand what "intrusion" means in this regard.
If you had gone to law school, you would understand that no right, whether constitutional, statutory, or held at common law, is unbounded. The government does have the power to trespass on your rights when they have a greater need to do so than your rights permit. When the Court calls this an "intrusion," what they mean to say is that it is a "stop" and a "seizure" within the meaning of the Fourth Amendment, but it is of such a small nature and character that it can be permitted.
There are other contexts in which we permit such stops -- the Terry stop-and-frisk, or even the probable cause search of a motorist. We do not, for example, require warrants when searching an automobile on probable cause because automobiles are readily mobile and the potential for the destruction or spoliation of evidence is too great.
If you were to look at the text of the Fourth Amendment, you would find it contains its own exception -- "unreasonable" searches and seizures. Obviously, a DWI checkpoint is a reasonable search and seizure as per our Fourth Amendment jurisprudence.
But shit, /u/ccmulligan, I never thought about the word "unreasonable" in there! Of course you didn't. You're a shouty libertarian on the Internet, not a lawyer. You don't know that "reasonable" is a term of legal art and something that is purposefully open to interpretation and case-based reasoning under the principles of stare decises. But you probably think that your definition of what is reasonable is so obviously and objectively correct, as you are so obviously and objectively the measure of all men, that you cannot fathom that jurists might disagree over what is reasonable and require a deliberative, adversarial system to argue over what is reasonable, and used principles of precedent and analogy to determine how a given legal standard should apply in other cases.
show me the specific warrant with valid probable cause that nerys71 was drinking and we therefore have the authority to stop him even for 1 second to ascertain his condition.
No one needs probable cause to stop you. They need reasonable suspicion, which is a very, very low burden.
License checks and registration checks are things you consented to by applying for a license and driving on public roads. When you engage in licensed and regulated activity, you impliedly consent to a higher degree of scrutiny. For example, I have a Texas concealed handgun license. I must present this license upon demand any time I am detained by an officer, whether I am carrying my weapon or not. Why? Because no one forced me to get that license. I obtained it freely, as was my right, but in doing so incurred a legal duty to provide it.
alas this is now what they do.
Because they can. Because that power is reasonable. Because virtually every jurist when confronted with this question would consider it reasonable.
Also, "alas?" Who are you, Benvolio? Talk like a normal person.