You've got it all backwards. On the wedgelive podcast, Sheila talked about having hot food and bathrooms for protesters. If the cops kill someone, a mayor who gets out on the streets and says "man this shit sucks doesn't it?" and provides actual resources is far more likely to deflate tensions than someone hiding from angry citizens and going on CNN instead of speaking to Minneapolis. People don't just decide to burn down city hall because they feel like it, it's because they feel ignored by the city not doing shit and egged on by cops shooting rounds in their faces. I've seen the cops kill enough people in this town to know it goes the same way every time, and early interventions can cool things off quickly.
You're really trying to say that if Frey just appeared at the third precinct it wouldn't have burned down? I don't believe that for a second. Far more likely is that Frey shows up, the precinct burns, and he's implicated in it.
A mayor can't effectively lead if they're being steered by the mob. This country gives too much rhetorical weight to "the people" who tend to be irrational, eclectic, and unreasonable. If Sheila wants to lead protests, she should continue being a community organizer, not mayor. Mayors need to lead on issues, not be a puppet.
It also just does not make any logical sense for a government to sponsor the protests against itself. At some point, it's just ridiculous. Even if 1% of protestors are out to cause trouble, the government would be actively implicit in that. The government shouldn't aggravate protests by using tear gas or shooting projectiles, but it shouldn't support them either.
It also becomes a question of which protests are enabled by government and which are not, which in turn becomes a constitutional problem. I somehow doubt Sheila would provide warm meals and bathrooms for pro-life demonstrators, which, no matter how you feel on that specific issue, is wrong. The city should not be involved in picking which protestors are winners and losers. Suddenly, "compassion for those protesting state violence" becomes a massive civil rights lawsuit.
It's just a bad idea. No other way around it.