Pro-police forces WANT mayhem. It makes people watching on TV afraid of the protests, and it changes the subject away from the widespread peaceful opposition to racist police violence.
Claiming "pro-police forces WANT mayhem" paints the situation in a very generalized, unhelpful, us-versus-them light.
There are definitely some pro-police forces that probably want some mayhem, for exactly the reason you state. There's probably others that want mayhem for other reasons. Across the board, however, I'd imagine most pro-police groups of people prefer peaceful protests that don't put officer lives at risk, not to mention all the collateral damage to protestors, buildings, economies, etc. that also could be avoided.
It's entirely possible (and, I'd argue, likely) that pro-police people aren't some homogenous group of schemers. You can be enraged about police brutality, abuse, and misconduct -- and also enraged by violent riots.
I know several people personally who say this exact phrase, yet they mocked the football players who took a knee during the national anthem at games protesting exactly this issue.
Obviously most sane people would prefer an effective and peaceful protest, but there has yet to be one for this particular issue. So I am hardly surprised it has become this violent, especially with members of the police force and the president antagonizing people further. Also, I would add that any protest of great size naturally has people who try to take advantage of it and turn to anarchy. Shutting down such rioters with force seems to exacerbate the issue, as police force is what is being protest—an understandably difficult predicament.