By the time the mtb gets there the suspect is long gone. My scenario is much more realistic.
No, actually it is not.
If a cop’s beat was strictly on paved roads and suspects had the courtesy to stay on those paved roads (on foot or on bike, and not in a car) while you chase them, then your scenario might make sense..... except that a car would work a whole lot better and what would the point be of being on a bike?
The whole point of the bikes is to expand the beat cops range.