By centralizing the police force, USA might end up might an entire state police force supporting a leader with autocratic tendencies, like what is currently happening in India.
Degree of police centralisation is similar between India and Australia. India does have city police departments, but they form part of and are subordinate to the state police, rather than being independent agencies like in the US–as such, the state governments exert more control over them than local governments. And Australian state police forces have local divisions too (Police Districts, Area Commands, etc).
Rather than India's police corruption problems being due to police centralisation, I think they are likely due to India's broader corruption problems, whose causes are much more complicated than anything merely to do with the organisation of its police services.
All other portions of government have cross-checks to stop people breaking the law. The police don't, and cover for one another.
There needs to be an organization that has clear and direct incentive to prosecute abuses by the police, that doesn't have a century+ long tradition of violence, selective enforcement, racism, and murder.
(Also, separately from the LECC, there is also an Inspector of the LECC, whose job is to investigate misconduct by the LECC themselves.)
(Inspectors General exist for for every federal agency)
There also has to be new crimes of negligence for things like 'body cam turned off' or 'records suddenly missing' and so on.
We even have a saying “counties are merely agents of the state.”
This is a Midwestern thing. The south has strong, independent counties.
The moral is that States, counties, and municipalities aren’t just “levels.”
In my state, there really is no state government above the county level (outside the state Capitol that is.)
There is an exception for law enforcement: we have state troopers and state department of investigation.
Neither are a substitute for local police.
This is very, very rare.
More frequently, we have county Sheriffs, not police. And their duties are quite distinct; only recently have they come to resemble police.
Shrievalty is more concerned with the functioning of the courts: sometimes holding suspects before trial (and maintaining jail facilites), ensuring the security and order of the court, protecting jury members from violent coercion, capturing fugitives, etc.
Patrolling and "preventative" enforcement is not a traditional role for the Sheriff.
For example, Polk County Sheriff (Florida) seems to be busy arresting people for DUI – https://tampa.cbslocal.com/2020/06/06/sheriff-grady-judd-54-...
Sacramento County Sheriff's (Calfornia) has a homicide bureau – https://www.sacsheriff.com/Pages/Organization/CID/Homicide.a...
Erie County Sheriff (New York) has a drug squad which regularly carries out undercover buy operations – https://www2.erie.gov/sheriff/index.php?q=narcotics-unit
Washington County Sheriff (Oregon) has a traffic safety unit – https://www.co.washington.or.us/Sheriff/FightingCrime/Patrol...
Many US counties have unincorporated areas, in which county sheriffs have full police patrol responsibilities. Often, that authority also extends to incorporated areas (villages/towns/smaller cities) which are too small to have their own police departments and rely on the county for all policing functions.
But I think that the distinction is still important as we talk about abolishing police.
Police, as an institution, are very new. Much newer than Sheriffs.
Is that historically accurate? Pretty much, yes. The modern concept of a police force only began in the 19th century, and at first they only existed in larger cities.
As separate police forces were established, Sheriffs began to perform less policing functions, and yield more of that jurisdiction to the newly established police forces. But, in many rural parts of the US, county sheriffs are the only local law enforcement, performing all police functions, and the same was true 150 years ago. The innovation of separate police forces never arrived in underpopulated rural areas.
So I think the history is the opposite of what you think–sheriffs performing general policing functions actually used to be more common than it is now.