Is there a framework—any framework, however hypothetical—that actually makes police accountable and subject to the laws they supposedly enforce?
But this goes back to government agencies never thinking about budgets. Modern politics is about marketing a tax reduction but never how that impacts the budget.
Markets are not perfect but on average they do a decent job of finding equilibrium.
“Democracy is the worst form of government—except for all the others that have been tried.”
Perhaps the only tweak would be to regulate these insurance companies to control their profit margins. We don't want to end up in the same situation as medical insurance in the US. Tax payers will have to pay some of the insurance premiums indirectly. So this idea can work well so long as insurance is in that goldilox zone: enough to provide incentive for the companies to exist, but not so much that their greed creates an even worse system.
The market model won't work because greed isn't real when discussing corporations. That's like calling a tree growing towards the sun "greedy." No, the tree is fulfilling it's biological imperative: put more leaves closer to the sun.
Corporations must maximize profit. The corporation that maximizes profit best is the one that can consume other ones and tend towards monopoly, the perfect state. All actions are permitted when fulfilling biological imperative.
So, trying to fenangle a market based solution to police brutality issues will result in a couple predetermined outcomes: insurance payouts won't happen because why would they voluntarily pay, furthermore, cop insurance companies would leverage their superior capital to lobby the government to protect their profit margins, which individuals can't prevent through market efforts or individual actions since the corporation's power is so much greater.
I actually think a system like this does a lot better than you might imagine. There are quite a few lawsuits for abuse of power beyond murder cases. It’s far from perfect but helps set the directional cost.
There's also an alteration to the interpretation of "reasonable expectation of privacy" that could be made (again, by Congress) to account for the total sum of information, rather than each individual piece of information in isolation. For example, I have no expectation of privacy that people don't see my license plate when I'm driving but I don't expect that a single person/entity would have all of the locations my license plate has been in the last 3 days.
The other clarification/change Congress could make would be to change the "reasonable expectation" test to something less susceptible to erosion over time. (I didn't used to expect I'd be tracked in certain way because I thought it would have been illegal but now I do expect it even though I still feel it's illegal). The reasonable expectation test encourages normalizing surveillance for as long as possible before it gets to court so that it's unreasonable to expect otherwise.
All of these things, of course, would be still within the grasp of investigators with a simple warrant which would normally take less than an hour to attain.
There's no reason the same doctrine couldn't extend to digital papers and effects.