Such overreaching warrants were called Writs of Assistance back in Revolutionary days. They were a major point of friction between the Boston colonists and the Crown (cf. James Otis, also Townshend Acts). The Fourth Amendment contains these words
... no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
specifically to prohibit the kind of general fishing expeditions that writs of assistance are. It is yet another piece of the Constitution legal sophists have been able to inactivate.