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Not often. I was heavily engaged in Los Angeles city government for over 20 years. I am a lawyer by training but pls don't hold it against me. As to your question, which is a good one, the answer is sometimes. The LA mayor and city council often tried to harmonize police deployment, training, etc with the LA County sheriff. But it was impossible. Maybe the geographic picture might help you see the complexity in LA. LA city is about 350 square miles with a population of over 4million. LA county is 4,000 square miles with an overall population of over 11million. There are about 88 cities within the County. Think of this like a huge piece of swiss cheese with the holes representing each city boundary and the solid areas the responsibility of the County. A number of small cities contract for the County Sheriff to be their law enforcement agency. But there are still roughly 65 cities with their own cops, including the city of Los Angeles. It just so happens and each city and county enjoy constitutional "police power' i.e. the power to maintain their own police force and other powers. So you get largely uncoordinated cops all over the county. It is a structural mess> Politicians view cops as necessary to cover their own ass. They do not get benefits from coordinating with other agencies. The state can change this with budgeted programs etc but state elected officials represent the various parts of this swiss cheese so nothing really happens. Full disclosure I taught some Urban Law sessions at UCLA law school many years ago. I hope this muddled picture helps you a bit.
In my opinion, policing has huge issues with not enough oversight, not wisely spent budgets, and not nearly enough training and qualifications as European countries for example. However, I think the biggest issue is that our Social system does not have nearly enough money and there's expectation for the police to handle everything >

Yes. When every little town has its own police force and everyone has to handle all their own administrative matters, hiring, training, etc you create a lot of inefficiency, variability in standards and performance and reduce the ability to do oversight. >

What would be the solution to that problem?
Centralized training and administrative services for multiple localities? That would save some money. >

I am from New Jersey, the land of endless local government, and the result of endless local government is crazy levels of inefficiency which cause high property taxes and governments so small nobody even sees the corruption. 
The average American town is around 6000 people. That’s way to small to justify a police department. Either roll up a few towns with a single police department or handle it at the county level. Have standards, training and as much administration as possible handled at the state level with federal guidelines that must be met and a system for federal oversight. 
Maybe start treating the police as professionals and model things more like how we license doctors, lawyers, accountants and such. >

I upvoted you and I see some merit in your argument.
It seems, though, that big metroplitan areas are where we have most of the crime because that's where we have most of the people.
THOSE cops are overwhelmed. They need more officers, and they need other responders to take over some of the problems cops have thrown in their laps.
They also need stigma-free, mandatory psychotherapy. None of this "I can take it, I'm a tough guy." Objectively, police need community support as much as communities need service and protection.
Also, no more "code of silence" or "you can't touch me when I commit crimes. I got immunity and a union." We need to KICK OATHKEEPERS out of the police department. No more gang members "moonlighting" as police officers.
Do I support the police? Yeah. Do I support the KKK and white nationalist weirdos? NO. >

Yes, we should have one state police with divisions for cities and rural areas.  New York as an example would have a very large force with multiple divisions.  Montana would maybe have two divisions.  However all would be accountable to their state legislature; have standardized enforcement, training, complain procedures ect.  
That would give us 50 police agencies and something like 18 federal departments. Much easier to manage in my mind. >

The large number of agencies reflects the nation's political design and structure. We have a federal government with several law enforcement agencies. Then we have 50 separate states each with one or more state law enforcement agencies. Then we have separate forces in big cities and an independent sheriff in most every county or parish (Louisiana). Add that up and you have the large number you cite. Jurisdiction over cases can open a can of worms. Each agency has its own training process and content with often very little coordination. Police unions also seek to maintain each law enforcement agencies' independence. Separate data bases are maintained. Thank God the FBI has developed a single source of data for some evidence (e.g. fingerprints). But otherwise we have a law enforcement tower of Babel. The best first step at coordination, in my opinion, should start at the state level. Training standards, code of conduct requirements,  data collection and more must be directed by the state. But this will be difficult in huge cities like NY, Chicago, Los Angeles who want their own police for political rather than law enforcement reasons. >

Have you every heard a politician discuss the need for centralisation or more coordination at a minimum? Or does it fall into the too hard basket for them?