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Well, the law is actually nowhere near as bad as you think. Messy, complicated, but not that bad.

The checkpoints are only allowed to check for driver's licenses, valid tags, and insurance cards. The police can NOT search your car without probable cause - while the cloud of dope smoke will net you an immediate arrest and search incident to arrest, for the alcohol they have to get you out and run the field sobriety tests and the alco-sensor and arrest you. And they can't do an impound search on your car unless there's nobody who can drive it home.

Otherwise, they can question you if they have an 'articulable suspicion' - called a "Terry stop" after Terry v. Ohio. The questioning must develop probable cause, or they must ask for and receive permission to search.

As for a speeding stop, once the officer has written the ticket and checked the radio for outstanding warrants, he may not 'unreasonably prolong' the stop to ask intrusive questions about other matters, to wait for a drug-sniffing dog, etc.

The checkpoints are only allowed to check for driver's licenses, valid tags, and insurance cards.
Do they ask you to show these? (Can I see your driver's license and proof of insurance?)
Or do they demand you produce them?
BTW, any drivel about "they're being being polite by asking for them" is not an argument. In matters of the law being polite is not necessary.
If they are demanded then "Show me your papers" comes to mind. Maybe that's why we don't have random search laws in Texas to date.
If the driver is asked for the information you mentioned above then hasn't the questioning already begun as soon as they are stopped, whether there is an 'articulable suspicion' or not?
You might find this article, dealing with 'articulable suspicion' as well, of interest...
'Open-carry' becoming central gun-rights issue
As the court noted in summarizing Mead's arguments, federal case law allows officers to conduct investigatory stops without a warrant only if "the officer has a reasonable, articulable suspicion that criminal activity is afoot."

Otherwise, they can question you if they have an 'articulable suspicion' - called a "Terry stop" after Terry v. Ohio. The questioning must develop probable cause, or they must ask for and receive permission to search.
Here is what I found for "terry stop" and it doesn't quite sound like what you're saying it is...though I could be wrong.
Terry Stop Law & Legal Definition
A "Terry Stop" is a stop of a person by law enforcement officers based upon "reasonable suspicion" that a person may have been engaged in criminal activity, whereas an arrest requires "probable cause" that a suspect committed a criminal offense.

It seems to me that a "Terry stop" is predicated upon "reasonable suspicion", it can't be developed through questioning. The suspicious activity must be observed before the questioning begins.
Surely simply driving on the roads can't give law enforcement officers any reasonable suspicion that a person may have been engaged in criminal activity, does it?

TERRY v. OHIO, 392 U.S. 1 (1968)
Suspecting the two men of "casing a job, a stick-up," the officer followed them and saw them rejoin the third man a couple of blocks away in front of a store. The officer approached the three, identified himself as a policeman, and asked their names.

And you seem to have a contradiction here...
The police can NOT search your car without probable cause... where you emphasize not, yet...
The questioning must develop probable cause, or they must ask for and receive permission to search.
...you say they must ask for permission to search.
Why do they have to ask for permission to search when you say they can't search without probable cause? If they have no probable cause to search your car why would they then ask to be allowed to do so?