> For example in Carroll v. United States, the judicial branch surrendered its authority to authorize searches to the executive branch.
The judicial branch can choose not to enforce the Constitution, contrary to its duty and purpose, but what they can't do—what no branch of the government can do without amending the Constitution—is legally authorize any agent of the government to perform a search or seize property (i.e. issue a warrant—whether they use that term or not) without "probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized." The text is perfectly clear and permits no exceptions or "carve outs". I doubt the intent was for the police to issue their own warrants, but even if the judiciary grants them that power they still have to fulfill the requirements.
Of course if you're just saying that what they can get away with in practice and what the Constitution actually allows are two different things, I agree. There are rights, constitutional and otherwise—and then there is power. Every time they do this, however, it undermines whatever legitimacy or respect they might have otherwise had. Any thug can steal your stuff or invade your privacy and have a chance at getting away with it. To the extent a government wants its actions to be seen as legitimate it can't afford to ignore that "piece of paper" it was founded on.
> The police, of course, determine if they have probable cause.
What counts as "probable cause" is indeed the weakest part of the 4th Amendment. At the very least, if a given "cause" does not lead to the target's conviction in a majority of cases, of a crime sufficient to justify the search, then you cannot reasonably consider it "probable". Unfortunately that can only be observed in retrospect. It would have been better to require full compensation to the victim for any search or seizure which does not lead to their conviction, ensuring that the incentives are properly aligned.