I think you could safely make the argument that during an inaugural event attended by virtually every elected member of the federal government and hundreds of thousands of people en mass on the streets in poor weather — A polarized election with highly charged opinions on both sides; A losing side that has already shown a propensity for riotous violence due to the election recently; News reports and video evidence of planned violence; protestors wearing masks, no real way to tell who ahead of time could possibly become violent…that police would be exceptionally cautious to not just maintain order, but quell violence and riotous behavior very very quickly.
Imagine if that violence was not contained and it spilled into the national mall. Conservatively, there are 500–600,000 people there — most support president Trump. Do you think 10% might defend themselves and retaliate? It would be a blood bath. I suspect the number would probably be higher.
The police are there to protect everyone, not just the protestors. Were they cautious and quick to control and contain? Of course, and thank God.