Sounds like the Mayor/Police wanted to avoid liability (first priority) and images of police knocking heads that could set off Baltimore style riots and looting (second priority, but now they can pretend otherwise). Inaction was a gamble, but much easier to defend to Charlottesville’s Leftist electorate than Bull Connor redoux.
The Mayor and Governor knew full well that trouble was brewing, but failed to manage it the event properly. Free speech rights could have been better protected by requiring the event to be held in a wide open space — not a tiny square amid city congestion (with jammed streets, cars to attack, buildings to burn, stores to loot), with a plan to keep the sides physically apart. Let all concerned yell and scream until they are tired, escort the pro-statue group away, and let the others go home. The tactics of crowd control aren’t new or secret. But the melee gave the media the desired story, so maybe they feel like it was all a success.
I don’t mean to be argumentative but the Mayor wanted them to move the rally to a larger park and they took it to court and won the right to assemble in the park with the statue. That said the police should have kept both groups apart no matter what and instead they pushed them together.