America's police system is actually really weird if you compare it to other parts of the world.
For example, in Japan the police have sweeping powers that most Americans would never tolerate, including powers to search without consent and other breaches of privacy. Yet their police are agonizingly sensitive to public opinion, and you can be certain that if an officer shot someone's dog in exactly this situation, their entire career would be over.
I can't say for sure, but I wonder if perhaps I wouldn't mind having fewer protections against things like police searches and whatnot so long as the police were actually concerned with maintaining a reputation of excellence and public service, and could actually be held accountable when they screw up?
(Although to be fair, I think part of that is they're in competition for the trust of the public at large - if the cops don't do their jobs properly, the people will go to the Yakuza to solve their problems instead.)