In English, you would use the word "agency" instead of "structure" to describe the police. I would also use the word "governing" or perhaps "organization" instead of "system" to sound more natural. I would simplify the last sentence.
The police are one of the most important agencies in the governing of any country. All countries have police agencies. If you ask me why, I'd say that without police, we'd have chaos.
Hope this is helpful