That was more or less my first thought, but most likely the result would be that it would never happen, because it is not so difficult for someone with a warran

That was more or less my first thought, but most likely the result would be that it would never happen, because it is not so difficult for someone with a warrant to search your house, to "find" something there. Right now, there's no motive, but if you knew that coming up empty would be, not embarrassing, but legally dangerous, the temptation to make sure you always bring backup evidence to be "found", would be large. I think it would make things worse, not better.