I would urge you to reread the 4th Amendment to understand what the Founders meant by a 'reasonable' search.
The fact that some cop or DA thinks it is reasonable does not make it so. Complying with the requirements of the 4th -- to obtain a warrant based on a sworn affidavit and probable cause and detailing the search and what is to be seized, is what makes it reasonable. Any search not complying to that is unreasonable
In one respect you are correct. Reasonable cause is not for the DA or law enforcement officer to decide. They prepare affidavits which are submitted to judges for scrutiny and, upon agreement, the issuance of the warrant. Unhappily, there are far too many instances where the legal scrutiny was cursory and the LEOs burst into the wrong location or entered with a totally inappropriate degree of force. But, that's another issue...
Suspecting you're interested in "natural rights", here's an article that disusses same in the context of the creation of the Constitution and the relationship between individuals, States and the Feds under same: http://www.cato.org/pubs/pas/pa326.pdf