The would still need a reason to stop
The reason to stop comes up only if your lawyer brings it up. A public defender isn't going to bring it up because it requires being able to build enough doubt to have the judge inquiry. And a judge is going to be less favorable in giving a benefit of the doubt for a public defender. If you cannot afford a lawyer, you're less likely to afford the filing should the court go down that road of police inquiry.
This is why most people who go with public defenders just go with simple bench arranged plea deals. The vast majority of people pulled over aren't going to have the resources to challenge this. That's the entire point.
You feel Florida being able to unilaterally dictate validity of state documents is okay?
— Article IV Section 1 US Constitution
— Article I Section 8 Clause 3 US Constitution
Florida doesn't seem to have authority to just unilaterally dictate these things. It would seem that they must work with Congress to implement such regulation. The entire point the framers of the Constitution placed on the State system in Article IV of the Constitution is to:
Florida's move to attempt to apply some pressure to citizens from other states is a direct violation of the core ethos that the framers of this nation wanted to have. If Florida wants to regulate Floridians into a fine mushy pulp, that is Florida's prerogative. Additionally, if Florida wants to prosecute someone from another State for violation of a law that Florida has, that's fine too. Where the line is crossed is when in the carriage of enforcing that law, it requires Florida to openly question another State's issuing documents. That is the violation.
Florida MUST work with Congress to implement the requirements for this framework that they have set up to function. Florida has not done so, they have forgone coming to the table to discuss the issue with the various States and decided to act in a unilateral manner. I get they want to clamp down on immigration, they must do so according to the laws that are set forth and must do so in good faith with the other States. This is neither.