Allowing police to search a location on a whim? True, it would catch some [NOT ALL] of these kinds of crimes, and undoubtedly save lives. But, it's a double-edged sword.
Some people in law enforcement have a lust for power, superiority, and authority. This apparently passes through the psychological testing before employment; some P. D.'s consider it an asset if a new hire is likely to be ruthless on his/her job. Though I am completely innocent (other than speeding or something), there is no time that I ever feel as UNSAFE as when I am stopped by a police officer. In some Departments, it has been alleged (proof is difficult! - the circumstances collude against truth) that some officers are carrying illegal drugs on them, which they can use in an "Aha! Look what I found in your glove box (or freezer, etc.)!" It's a strong revenue cash cow for cash-strapped cities, etc., because they can trump up the charges to trafficking, and seize your car or your house by using the old admiralty laws (??) which the Courts have generally said are OK to use.
The court docket may be something like "City of Memphis v. 2008 Corvette registered at 311 Maple Street" and of course the City will win because the Corvette cannot talk or hire an attorney. I still think this is Unconstitutional. I remember about 25 years ago that an entire private planes-for-hire company was seized in Peoria because one of the planes he had rented to somebody was used for drug trafficking, flown to Las Vegas. (The landlord, or the lessor, cannot possibly ever know all of what's going on!!) I have also heard about stories in my region where an entire apartment complex is seized (and dozens of families are kicked out and made homeless) because somebody was busted dealing drugs in one of the apartments.
Furthermore, many prisons are profit-making, and they want to jam as many people into their prisons as physically possible. Arresting people capriciously (almost always under the rubric of the damned War on Drugs) is one h-e-doublehockeysticks of a cash cow for multiple entities and layers of administration, also including politicians - and, in some places, judges - who will gladly play the "tough on crime" card in re-election campaigns.
This is what would be happening all the time if the cops were allowed to search places without probable cause.
I should add, though, that a naked woman crawling around in the back yard (most likely not in some ordinary way such as preparing to sunbathe, but probably under extreme duress), seems like adequate proper cause to me.