There are some technical notes, most of which would be way too boring to show (like cop shows almost never show scenes of doing paperwork).
1: Does Johnny have the credentials? To run a Dojo, you have to be at least a 3rd Dan blackbelt. Seems to me that after losing the tournament, Johnny probably left. Did he study somewhere else?
2: (and this ties back to the original movie), no one under 18 should have a blackbelt. Period. How can you master the basics (ie: what is required to get said shodan rating) when you body is changing on a monthly if not weekly basis. My own instructor, in 45+ years of teaching, only ever awarded 1 blackbelt to an 18 year old, and he was exceptional (it wasn't me). Blackbelt requires 4-7years of training for 1st (shodan). 2nd requires a couple more (sometimes there's a half-step called Shodan-Ho). 3rd requires a few more years. So, assuming there was any legitimacy to Cobra Kai, Johnny would have had to train for about 5-7 more years after losing the tournament. Did he? Somehow I don't think he'd want to train with Kreese after being strangled by him.
3: Cobra Kai is a copyrighted organization. Johhny would have to file paperwork with them. Otherwise they can go after him for copyright infringement.
4: Johnny would also have to file paperwork with one of the Japanese international karate associations.
5: Johnny tells his student without showing him. The kid clearly doesn't know how to make a fist, and he doesn't know how to do push-ups on knuckles. He tries to distribute his weight across the whole hand rather than properly focusing on the Index and Middle finger knuckles.
I am beginning to be concerned about the quality of what is shown here.
Of course, all of that is just the first student. Johnny is out of practice, and clearly has no idea what is required in running a dojo. Somehow, I don't think Kreese had his advanced students teaching the beginners (something that is supposed to start at 5th kyu/green belt)--that would have been yielding or sharing power.
Johnny didn't know he had to have a license and insurance. I don't know what the writers of the show do and don't know, but I think the straightforward interpretation is that a washed-up former karate guy got some money and said, "Hey, why not?" and is totally over his head.