Exactly: this should really be in the realm of criminal prosecution, not civil suits, in which case the positives of qualified immunity could remain in place. But we have such a toxic, broken, in-group culture in our police force that we cannot rely on self-directed justice to happen. So I think we have no other option but to open the floodgates on civil suits.
Anyone can make a complaint to them, and they will investigate, and if they believe the law has been broken, can prosecute individuals (in a regular court) or fine police departments as they see fit.
Both my parents were retired Police, and I know there's a lot of good people that work in those fields. I also know that not every community, situation or person is the same and there are a lot of people on power trips that even fellow cops don't always like. It's often hard to speak out from within a group.
Some of the more recent events are particularly grievous and should absolutely be prosecuted... There are many more incidents that should be as well. I tend to say it's rarely (though sometimes is) about race, it's usually a matter of blue vs everyone else.
As a practical matter, if there is possible liability, everyone will have to have liability insurance, just as in the medical professions, for example.
Every police department with more than a couple officers has an official structure for reporting abuse to leadership (either police leadership, or civilian leadership). State agencies and police forces absolutely have jurisdiction to investigate local departments, and the FBI and DOJ can investigate anyone they want.
I suspect the mistake in the US is that all the people who could punish the police are 'too busy' with other things. Make a dedicated team who has nothing else to do, and suddenly they'll be snooping around like journalists looking for dirt so they can make a conviction and get a promotion.
FBI doesn't want to investigate LAPD. They need LAPD, down the line, when there's some case for which they'll need cooperation.
What's needed is a Federal policing agency tasked with investigating and prosecuting police misconduct. That's the whole remit; police misconduct is their alcohol, tobacco, and firearms.