Edited to Add: I cleaned it up a bit, corrected some dates. Feel free to use it and spread it around.
I can't answer for everyone. But, here is my reasoning.
1. Counting from the Norman Invasion in 1066 to our federal Bill of Rights in 1791, it took 725 years to wrest rights away from government.
Magna Carta in 1215 was a big step. As were the English Civil Wars in 1642-48 that struck a blow against the divine right of kings to rule. Another big step was the English Declaration of Rights of 1689 arising from the Glorious Revolution that kicked out James II.
In between Magna Carta and the American revolution, other rights were wrested from government one little piece at a time. Some examples:
The abolition of the Star Chamber court (tied to the 5A right againstself-incrimination);
William Penn's trial for preaching Quakerism (tied to 1A right of religion);
William Penn's jury cementing the power of a jury to judge an unjust law and the power to refuse to convict for violation of an unjust law (those jurors were literally imprisoned—“without meat, fire, and tobacco”--to coerce them to give the verdict the judges wanted, and a few were prosecuted for not giving the verdict the judges wanted);
Peter Zenger's case where writing the truth was not a defense to a law against seditiously libeling the government (tied to 1A free press rights);
The 1760's case where a lawyer named James Otis argued for hours against general warrants, a young lawyer named John Adams in the gallery who would later say the spark of revolution was born in that courtroom.
The list goes on. One right or a piece of a right at a time across centuries, nearly 800 years from Magna Carta to today. Eight. Hundred. Years.
A lot of people suffered for lack of rights. A lot of people died winning them.
Since the Founding over a million Americans have died defending our rights.
Just the cost in blood and treasure to obtain and maintain rights makes them incredibly valuable; and this is before one prices how much he values the freedom they guarantee.
An individual cop's desire for information pales into insignificance when weighed against the history and cost to get and maintain rights.
"Officer, no offense, I know you are just doing your job, but over a million Americans have died defending these rights. I'm not going to spit on their graves by waiving them."
Or, if the officer bugs me further, "Oh, I'm sorry officer. I am a patriotic American. I will cooperate with you to the full extent required by our laws." (followed by polite silence)
2. If you give identity info when not required, it can come back to bite you. It hasn't happened often; rather rare in fact, but its there. The cops may not be able to figure out something to charge you with during the encounter itself. But, afterwards they may talk to a prosecutor, or have some time to research and think, and then come up with some charge. Now they know who you are, where you live, and where to serve the warrant. It happened to an OCer in California a couple years ago. The prosecutor even got the trial judge to agree to twisting the meaning of the word "public" to make the charges stick and obtain a conviction.
In a court case called Hiibel vs 6th Judicial District Court, the US Supreme court even acknowledged that giving identity info might lead the cops to something more, basically turning it into a self-incrimination issue.
Regarding identifying yourself, you have to decide for yourself which is riskier, giving identity info or not.
Also, you want to make really sure about the state and local laws in your area. There are plenty of places around that require a person to identify himself to a cop, and have penalties for violating their law. Sometimes the penalties are rather stiff.
If you are unsure, you can always say, "Officer, I am providing this information against my will. I will comply, but I do not consent." (give the identity info). Then you would be safe from being charged with failing to provide identity if there happened to be an identity law in that jurisdiction. Plus, if it later turned out there was no identity law, or the cop didn't have sufficient legal grounds to demand your identity, then you would have some ammunition for a formal complaint, or another point for your lawsuit.