The most successful police bike of all times was the Raleigh DL-1 used by police throughout the British Empire. Millions were made (and are still made in Denmark). The front fork extends out, absorbing shock of cobblestone streets much better than road or sport design bikes. The frames are strong as were all the components. The internal hub gear required less maintenance, and they were primarily intended for flat areas where serious braking was not important, and weight was not a consideration. They were tools, not toys, thus one can buy a 1950's, or 1930's model and refurbish it, whereas the typical life of a modern bike is perhaps ten years at best.
Today, police use MTB because that is what is on offer. MTB are strong and durable, but not made for the purpose of patrol. This is typical of America, where, for example, taxi cabs are consumer cars; in contrast to the London cab which is purpose built for taxi (high ceiling, large rear space, very tight turning radius, designed to not exceed speed limits, unique look to be easily spotted).
Unlike the UK, in America police departments are small and very local, with overlap of town cops, county sheriff, state police, college police, airport police, etc. Thus, no one has the purchasing power to specify purpose-built, and the bike industry still is a fashion-follower rather than a serious tool maker as it was from Victorian times through the 1950's (except in America where the bicycle business was primarily a toy maker for kids until they got their drivers licence).
Raleigh DL-1