You've provided the theory, but you didn't answer my practical question: you have 1000 people representing authority and 100,000 people crowd. Let's say 4% of that crowd is violent. That is still 4 times your capacity. All while a large number of the remaining 96k are shouting at you. Put yourself in the shoes of those 1000 and your task being "restore order". In which case, the ball is in the crowd's yard. As an outside spectator(and someone who literally grew up in the epicenter of daily protests as a child), what I'm seeing here is the recent South Park episode turning into a documentary.
It's really easy to quote laws and rules, but in the real world, they are not always applicable. And in the case of mass gatherings, they are hardly ever applicable. Are you seriously suggesting that you were never put in a position where your only course of action was to grossly break the rules? If so, I envy you, I really do. No one hates breaking the rules more than I do but on many occasions in life, I've had to. It doesn't have to do with how rules and laws are defined or implemented. It's simple math: you have two bricks and three holes to fill, otherwise your house will flood. It's the same story with the pandemic - no one wants lockdowns or businesses crashing but it's either that or the death of millions.