They say assign a police officer to each school, but they don't discuss that police have no authority at all.

Are you going to put an unarmed police officer at the door just to be a barrier?
Let's assume that the government, as you say, finds your idea reasonable and assigns a police officer to each school.
If the police search your underage child, you'll say they have a grudge against me and are bothering my child, or you'll accuse them of harassment, or if you can't call someone younger, you'll complain to CİMER.
And if you don't do any of these, you'll say, "I pay their salary, you can't search my child."
Let's assume that police don't search anyone and aren't doing their job; you'll ask why they are getting paid.
The problem is you, us. The problem is the system.