Homicides went up in 2020 and 2021 and are now rapidly coming back down. Violent crime nationwide hasn't increased. But the perception of a crime wave still colors U.S. politics.
Perceptions of crime waves are mostly driven by propaganda, not measurement.
In some cases, a "crime wave" doesn't represent an undifferentiated mass phenomenon, but rather the behavior of a single organized crime group: it's not that "everybody is being more criminal today" but rather "there is a specific gang that has figured out how to get away with a lot of crime". This seems to be the case for a lot of property crime in my part of the country.
And it's usually stopped pretty quickly too. Remember all that catalytic converter theft in the Bay Area? They caught the middlemen buying most of them and suddenly no one talks about it anymore.
But maybe, the rising in police killings kills more murders before they could start their murdering, so the rising in police killings could save more people than the police is killing.
/s
Something that is worth mentioning is that the general mental health of the nation has gotten much worse too. Suicides from 2000 and 2020 has increased from between 30% and 60% (varies from source) indicating a deteriorating mental health of most citizens. This often in turn causes people to think and act irrationally or dangerously. This also correlates to the struggles of the pandemic, many people's mental health suffered during the lockdowns and during this period murders, police killings and suicides spiked during it.
Does this mean the police are perfect? Not necessarily, but when it comes to most trends and phenomena it's generally unhelpful to pin the blame on individuals instead of a more nuanced and informed explanation.