The Founding Fathers never wanted a national police force. In fact, there were adamantly opposed to the idea, having a strong distrust of centralized authoritarian structure.
They specifically left out the powers to form any kind of national structure for domestic policing, leaving that entirely up to the states, with one teeny, tiny exception -- this bit of power ceded to the federal government in the Constitution:
To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes;
The Commerce Clause, it's often called. And for many years, that worked just fine, and was accomplished without any national force. It wasn't until 1865 that the Department of the Treasury established the Secret Service to combat counterfeiting -- a relatively easy fit for the role of "regulating commerce among the several states." In 1908, the FBI got its start (although the name was different then) with a grand total of 10 agents.
Read More