No, the US should not do this. It would violate our system of federalism and would be extremely unwieldy as well.
Our system is based on federalism. Our different states have different laws and different law enforcement priorities. For the most part, issues of policing and crime are left to the states. There are crimes that are federal, but the vast majority of criminal law is state law. Therefore, police should be controlled on the state and local level.
In addition, our country is so huge and has so many different kinds of communities that it would be very hard to have a "one size fits all" police force. The police force for the community of 2,000 people where I teach and the police force for New York City are going to be so different that putting them together under the supervision of one agency would be pointless.