The issue with this series is the blurred line between the fictional and realistic aspects of the story and the world it's placed in. This comes from the tone of the original movies, which was necessary to quickly and easily set the tones for the characters. In Karate Kid 1, Kreese was never really seen as more than a narcissist, as he is a background character, keeping the focus on Johnny as the main antagonist; until Karate Kid 2, when Kreese is shown to have turned on Johnny for losing the championship. This then makes him the bad guy, and Johnny then doesn't seem so evil.
Realistically, Kreese would have likely been arrested for that behavior. But he is simply left without students, and nothing else happens. You might argue, that when we learn that Kreese is a War Veteran, that he received special treatment in this situation, but this isn't true. If anything, he would have likely needed to go into hiding, have people bail him out, or something similar for him to maintain his freedom, but even then, he would have still been deeply frowned upon by society. Realistically, the only way that Kreese got away with this, was for his students, Miyagi, and Danny (and any other witnesses) to just say nothing. Again, highly unrealistic.
So when it comes to the TV series, this fuzzy "reality" line is carried over. Things such as
when Kreese released pythons in the Larusso Dealership as a "threat"
it warranted no further investigation - no one complained to the police, it was simply a "They will pay for this" reaction. Or,
when Miguel ends up in hospital at the end of season
the school is punished for not having tighter restrictions, even though the students are highly skilled fighters, and the brawl is highly targeted between two sides. This is clearly some kind of Gang War, and highly dangerous, that leads only to one arrest.
As you yourself pointed out, when Demetri gets punched in the face, he doesn't go to the police, and that makes no sense. He was assaulted, and makes no effort to deal with the law.
So basically, the "reason" that no one is arrested, when it seems like they should have been, is because the line between real, and unreal is too blurred, and it becomes confusing as to what should happen, and what actually happens. The unrealistic story exists in a realistic world; and if anyone was arrested, like they realistically would have been (even Danny Larusso would likely be arrested for his part in the whole outcome), then the underlying story (of the conflict between Danny, Johnny, and Kreese) would be very different, or even non-existent.