There is a misunderstanding compared to OP's intent. It's not that separating military and police guarantees that the police will make the police serve and protect the people. Rather, if separated, police has a better chance to serve and protect the people, compared to a situation where it's the military's job.
Consider the the separation of church and state. It's done so the government remains neutral in religious matters and does not favor or establish any religion. In reality, some churches are clearly favored. Or the review system in academia. Peer reviews are so that bullshit doesn't make it into published papers. Yet, bullshit and bias does make it into published papers.
This is just a system that is working somewhat well. With obvious, very large room for improvement. But the direction, separating military and police, is good. Just not enough.
Consider the the separation of church and state. It's done so the government remains neutral in religious matters and does not favor or establish any religion. In reality, some churches are clearly favored. Or the review system in academia. Peer reviews are so that bullshit doesn't make it into published papers. Yet, bullshit and bias does make it into published papers.
This is just a system that is working somewhat well. With obvious, very large room for improvement. But the direction, separating military and police, is good. Just not enough.