Would combining city, county and state law enforcement be a good idea?
Combining these forces would result in more efficiency both in terms of money and in terms of coordination. As it is, there are so many law enforcement agencies that it is likely that there are positions that are duplicated unnecessarily. Having a police chief, for example, in a city with three police officers (like the one where I teach) is unnecessary. If agencies were combined, this sort of duplication and waste could be eliminated. In addition, there would be fewer problems with agencies failing to communicate with one another or competing with one another in ways that reduced overall efficiency.
The previous answer is not right in that cities and counties are not sovereign. They exist only because the state government says they exist. States could combine their law enforcement agencies if they wanted to.
The major problem would simply be that people at the lower levels (city and county) would feel that they no longer had as much control of their local forces. They would feel that their police were being controlled from afar and might well feel that the police were, as a result, less responsive to local concerns.