The mayor's request was basically that the Feds not unilaterally start escalating and militarizing police efforts in her jurisdiction without her involvement. In hindsight, that does seem to have been the correct strategy for her police department, because all the violence seems to have been concentrated within the jurisdiction of a different police department.
They could have easily guarded the building itself. Close the doors and post 30 guards at each entrance?
Based on the reports, some of the rioters were carrying blue lives matter flags. I would say it's pretty obvious there were shared sympathies between the mob and those protecting the Capitol.
Being overrun by attackers is one thing. Ignoring them would be dereliction of duty. But assisting and siding with them? I don't even know what you'd call that anymore.