The value of a cop on a bike who can just put a foot down and stop and talk to the public is HUGE
Especially in urban environments where police are accused of being distant from the population
It's why cops used to have foot patrols. So they would walk around and interact with the community, make friends with people sitting on their porch who would tell them when something wasn't right. It was healthy.
Then cops started driving in cars and that interaction stopped. Police started being less trusted. The relationship with the public became toxic in a lot of places.
But on a bike...that's all back. You now have a foot patroller who can cover 10 times as much ground without giving up that friendly face that talks to the public.
Baltimore has them, but only in the touristy spots. Bikes are great for interacting with people and keeping purse snatching to a minimum. They aren't so great in hardened drug neighborhoods controlled by gang violence. Cops still use cars in those neighborhoods.
As for a cop's speed on a mountain bike....they spend all day every day on that mountain bike. I'd venture to say they can ride that mountain bike faster than most human beings can ride a road bike.