There are many fictions in the law, the most dangerous one being that the government is your friend, and the related one that the government has interests other than protecting and serving its own agenda, and other than expanding its own turf. It is not your friend, and it does not have other than self-regarding interests.
Recall that the Founding Fathers of the Republic considered government to be evil, sometimes a necessary one, and sometimes an intolerable one, but evil nonetheless. So, for people to assume that objective "good" or "truth" comes from evil is naïve. That is why the Framers installed the common law jury of peers into the Constitution, to place citizens as a protective bulwark between government and the people's liberties.
Unfortunately, too many jurors think that government is good, and truthful, and altruistic, and they accordingly do not approach their tasks with the institutional skepticism that the Framers intended.
And too many individuals, when confronted by cops, think they are social workers or pastors and think that being helpful and upfront about what the cops want will serve them well. It never does. The police are talking to you to put a case together, period, end of issue. And if they can put it together by getting you to spill the beans on yourself, or on your friend or loved ones, their job has just been made easier.
One can be cooperative without being self-accusatory. "Yes, Sir; I choose not to speak with you, and I choose not to let you search" is not a lack of cooperation: it is the self-protection the Framers installed in the Constitution. "Oh, yes, I'll tell you what you want to hear and I'll let you search wherever you want" is not being cooperative: it is being stupid.
Another fiction is that, when push comes to shove, judges will protect you. WRONG! Judges are part of government. The Framers might have had a view that the judiciary would protect individuals from a self-regarding and rapacious executive, but that is not reality in these increasingly political times. The judiciary by and large defaults in the direction of power and away from liberty.