Without the exclusionary rule, not only would the people not be secure in the persons and property from unreasonable searches and seizure (an ideal which is impossible to attain, though obviously necessary to strive forward under the Constitution) but would be deprived, by government, of life, liberty, and property -- through the criminal process -- without due process of law, insofar as they would deprived of such as a direct result of government exercising powers which are strictly and expressly outside of those permitted to it.
> We are one of the few western countries to have it; it's an idiosyncratic response to the problem it addresses.
The United States is unusual in the world (including among "western countries") in the degree to which limited government is a foundational principle. Even other countries with a strong attachment to the idea of fundamental rights often have strong foundational attachment to ideas of governmental (e.g., parliamentary) sovereignty and supremacy, with boundaries of rights and limitations on actions of government agents being determined through the regular legislative process and not being fundamental limits on government.
The question isn't "why do we have 4A" or "why should we be concerned about due process". It's "why do we have this idiosyncratic rule, as opposed to the other obvious remedies to illegal searches, and how does the rule follow directly from the Constitution, which mentions it never?"
The usually offered alternative remedy is not actually a remedy to the problem, its a remedy to a different problem (and one which has an insurmountable agency problem in a system with a unitary executive).
> The question isn't "why do we have 4A" or "why should we be concerned about due process".
Which is fine, because I didn't answer that. I answered why the rule was essential to protecting the limitations on government in the Constitution, including due process, not why we have the 4A or due process.
> It's "why do we have this idiosyncratic rule, as opposed to the other obvious remedies to illegal searches, and how does the rule follow directly from the Constitution, which mentions it never?"
I never claimed it "flowed directly from the Constitution", so to the extent that is your question, it is a non-sequitur where the question was offered. I have answered why the rule is essential to implement the restrictions on government in the Constitution. If you would like to pose a counterargument, or challenge any part of the answer, please feel free and we can have a productive conversation. But merely making oblique and unspecific references to alternatives is unproductive.
I think you misunderstand what the rulebook is. The most basic "rulebook" in the US, and the one on which the exclusionary rule is founded -- the Constitution of the United States -- does not limit the actions of individual government agents, it limits the power of government. If you allow the government to use evidenced gathered outside of that rulebook, but punish government agents, you are, indeed, throwing out the rulebook, and the entire idea of limited government.
A central idea of the US system of government is that preventing tyranny by unbound government is more important than punishing individual wrongdoers in the criminal justice system.