Fourth Amendment traffic stop followup question

Question

This is a follow up question from why doesn't the 4th amendment apply to traffic stops.

So, the current answer states that the 4th amendment applies to traffic stops, which makes sense to me. So after thinking about that and looking up some odd articles that arguably make sense, I'm kinda curious of one of the issues that can arise from that.

Question: During a legal traffic stop, let's say that when they ask for licence and registration, you ask

can these documents be used against me in the court of law.

It seems the answer would have to be

yes

Since they can and if you were to receive a ticket, they would be a part of the evidence. Assuming you give them your identification information since you are being detained and investigated, how can an officer handle such issue of not violating the 4th Amendment?

Issuing a ticket for failure to have insurance would seem to have no basis since there is no proof, and requiring the proof would require either a warrant or the person to give up their right?

This is a theoretical question about individuals and their rights and I do have full insurance and produce it every time. I'm not looking for answers that involve the driver to forfeit their rights (i.e. "I would just hand it over", "issue the ticket, and let the courts hash it out", etc). I think we can make a safe assumption that the person is a reasonable person that likes to preserve their rights. And again, this is from the perspective of a honest police officer that would like to keep the person's rights intact. I will flag answers that go down that road as not an answer since they clearly would be opinions.

Answer 1

See Rodriguez v United States 575 U.S. ___ (2015). It has language describing the extent to which a police office can make "ordinary inquiries" incident to a traffic stop (internal citations removed):

Beyond determining whether to issue a traffic ticket, an officer’s mission includes “ordinary inquiries incident to [the traffic] stop.” Typically such inquiries involve checking the driver’s license, determining whether there are outstanding warrants against the driver, and inspecting the automobile’s registration and proof of insurance. These checks serve the same objective as enforcement of the traffic code: ensuring that vehicles on the road are operated safely and responsibly.

The touchstone of the Fourth Amendment is reasonableness. The government is only prohibited from unreasonable searches and seizures. Warrantless traffic stops are allowed if the officer has a reasonable and articulable suspicion that the driver has violated a traffic law. Once stopped, the officer can make "ordinary inquiries" described above.

Regarding Fifth Amendment concerns, the Fifth Amendment's document-production privilege does not apply to regulatory type records that are required to be kept by law or items analogous to a required record. Baltimore City Dept. of Social Services v. Bouknight, 493 U.S. 549 (1990)