Yup. It is going to be difficult to untangle to get anything solid.
I was reading an article a while back how as crime goes down, government want to cut the budget on police. So in theory, if crime rate was directly related to police spend, as spending goes up and down, then crime rate would follow the same approx curve, but would lag. But crime rate and police spend are not directly related. Because as you say, lets throw covid in.
The Fergusson effect yes. But that is not related to spend. That is withdrawal of policing from a segment of society. " The black folk are protesting, so stay away from the black folk". So a black woman phoning the cops because her ex threatened to kill her is probably not treated the same as in normal times.
And the list of variables goes on as you know. The type of policing, economic demographics, and how the police spent the budget.
And that is what defund the police was all about. Changing the style of police. From being heavy handed in tanks, going in guns drawn, to spending a reduced budget on cops with guns and spending more on the root causes.
And that last bit, the root causes would take time. And it can't really happen with Trump in the Chair. Because he tells the states to spend more on heavy handed cops or he will defund the state.
So yup. I agree. Accurate studies are near impossible to do.