So why exactly are so many cops in the US fucked up?
How many are? Roughly 1.1 million police officers(state/local) in 2008. What percentage of them are fucked up? If you're basing your math on what you see in the news then roughly 99.9999% of cops are fucked up because those are the high-profile stories. You don't hear stories about all the other cops.
I think the problem(s) are a lot more complex than "a lot of fucked up cops".
One of the core problems is that in gun-friendly America cops who take chances are cops who get shot. Way too many handguns out there. Handguns that can be in a purse, waistband, backpack, etc. That means the rules of engagement favor overwhelming force when in doubt. You see a 5-foot-2 teenage girl. The cop sees somebody with an open pack who didn't hit the ground when the cop yelled at them.
Realistically, it doesn't matter that she is a girl, it doesn't matter that she is black, it doesn't matter that she is a poor fit to the description of the person they were looking for. She's in the way, she's a threat, and she's not doing what the cops tell her to do. I'm not saying this is right or wrong, I'm saying this is the way it is. Cops are trained to respond with overwhelming force in that situation. I think he showed pretty good judgement going with the dog over the taser or the baton. See, I'm not even considering whether he should have done nothing at all. The rules of engagement said he had to do something.
This isn't a "bad cop" issue. This is a reality of policing in the United States, particularly in high-crime areas.
You want to change that? For starters significantly reduce the number of unregistered handguns floating around---good luck with that---even if you could get a Republican-controlled government onboard it won't matter because we're going to be 3d-printing handguns with Office Depot level tech any day now. Secondly you need evolutionary advances in defensive gear. If cops don't have to fear for their life in every encounter then you can go with much more passive rules of engagement.
All that said, I'm sure there are plenty of "bad" cops. Bad people exist in all professions, after all. That doesn't change until you start hiring machines instead of humans. You do what you can to weed them out but it is impossible to get all of them before anything bad happens. Do police protect their own? Of course they do. Is every incident like this where the officer doesn't face harsh punishment merely a case of protecting their own? Yes and no. If an officer is following established procedure he/she isn't the one who should be the target, of course you protect that officer. This case, it appears to me the officer was following procedure. We don't have to like that procedure, but we do have to take it into consideration when trying to judge the officer, don't we?