Why does Daniel choose the Crane Stance and kick in the final round? As has already been noted, the move is obvious and nigh-impossible to execute. Simple: Due to the "Sweep the leg" move, Daniel's left foot can no longer support his weight, but rather than throw in the towel, he gambles everything on a desperation move, the one move he actually has a chance of performing. And it works.
It seems highly unlikely Daniel, even with a couple of months of training with Mr. Miyagi, would have been able to beat the Cobra Kai dojo. However, there's multiple factors at work. 1. Daniel is working (however unknowingly) on perfecting his technique through disciplined repeated repetition. 2. Kreese is teaching his students raw brutality over discipline. 3. Kreese disqualified his second best guy in order to cheat. 4. Lawrence is clearly freaked out and upset about how the fight is going in the final round. Daniel's victory is as much about Miyagi being a better teacher and Kreese being a self-destructive fraud as it is about being better than his opponents.
Plus, the Cobra Kai dojo isn't a neighborhood institution. It's very possible they've only got several months ahead of Daniel themselves. It's not like they've been training since childhood under Kreese. Furthermore, Cobra Kai establishes that Johnny joined the dojo in 1979, while some of Tommy's lines in "Take a Right" indicate that he joined some time after Johnny, so it's still possible that some of Johnny's gang may not have too much of an advantage, time-wise, over Daniel-san.
There's also everyone's levels of exhaustion to consider. Everyone was fighting through all the prior qualifying rounds, meaning everyone was tired by the time the semifinals and final rolled around — but Daniel had been doing almost nothing but training all day, every day with Mr. Miyagi. Wax On, Wax Off wasn't just about building muscle memory, but building Daniel's conditioning and physical strength and endurance. The Cobras are probably only having two or three classes a week, and spending the rest of their time doing typical teen things. Daniel had spent as much endurance as Johnny come the final fight... but thanks to Mr. Miyagi's approach to training, Daniel had a much bigger endurance pool.
This actually connects to why the Cobra Kais and Daniel dominated the tournament: in most "traditional" karate schools the training tends to neglect physical conditioning, but the third movie and Cobra Kai establish that Kreese, and Johnny after him, do in fact use physical conditioning, and, as pointed out here, traditional Okinawan Karate such as Miyagi-Do did the same, leading to Daniel and the Cobra Kai pupils simply being stronger, faster, and having more stamina than their opponents. In addition, most schools have students who come and train for a few hours a week, whereas Daniel spends all day every day building stamina. And at least at first, it's quite possible that the Cobra Kai pupils were caught by surprise when Daniel proved himself their equal if not their better in terms of physical conditioning.
The tournament rounds also helped Daniel out since he had to fight Cobra Kai students in multiple matches, which consequently gave him experience in countering the Cobra Kai style. On the other hand, Johnny had only fought Mr. Miyagi in a one-sided fight that ended in Miyagi's victory, so he had to play catch-up in figuring out Daniel's techniques.
Why is Kreese so insistent that Bobby injure Daniel, in spite of Bobby's insistence that he could beat Daniel in a fair fight? Because he's trying specifically to get Johnny to come out on top. With Bobby out of the way, an injured Daniel has to go up against Johnny, seemingly sealing the latter's victory. While the twisted Like a Son to Me attitude that Kreese has towards Johnny in Cobra Kai wasn't on the writers' minds in 1984 note In fact, Johnny had basically zero redeeming qualities before his Graceful Loser moment at the end of the film; the idea of him seeing Kreese as a father figure was William Zabka's own invention, only made canon three decades later, Kreese's actions retroactively make a lot more sense in this light. Really, it'd be almost Heartwarming in Hindsight if it wasn't, well, Kreese.
Not only that, but Kreese is also punishing Bobby for not conforming to Kreese's Cobra Kai philosophy.
Bobby has shown himself repeatedly to be the least aggressive of Daniel's tormentors, often trying to get Johnny to back down when it's clear Daniel's in no condition to fight back. And right after getting disqualifying himself, Bobby is heard saying "I'm sorry Daniel, I didn't mean it!" repeatedly before he can leave the mat. And he's also shown this away from Daniel: notice how in the class that Daniel and Miyagi happened to see, Kreese had Bobby spar Robertson, a green belt. Bobby scores a point, hesitates, and Kreese looks at him and says, "what are you looking at? Finish him!" to get Bobby to finish Robertson off. This isn't a Cobra, "A true cobra feels no sympathy for its meals," as Kreese says to Hawk in Cobra Kai season 3 after expelling Bert for refusing to feed a mouse to a snake.
Early in the tournament, we see Bobby score a point against an opponent, and looks like he's going to punch him in the face before holding back. He then looks to Kreese, who stares him down and gives a stoic clenched fist of disapproval, as Bobby looks back smiling, trying to win Kreese's approval.
Throughout the tournament, Bobby has a smile of excitement on his face, while Johnny looks serious and intense. Kreese sees Johnny as his protege who has bought 100% into his Cobra Kai vision and what he wants from his students, much like he'll show with Tory Nichols, Kyler, and Johnny's son Robby Keene. In Bobby, he sees a threat similar to what he'll see Miguel Diaz as in the future: someone who has the talent to win (and Miguel wins his first All-Valley), but who won't carry on the Cobra Kai values, which could threaten the whole dynamic of what Kreese wants moving forward. By telling Bobby to disqualify himself by injuring Daniel, he kills two birds with one stone by not giving Bobby or Daniel the opportunity to affect Cobra Kai.
Bobby is confident that he could beat Daniel in a fair fight, protesting, "But sensei, I can beat this guy!" when Kreese tells him to put Daniel out of commission. Kreese believes that too, but he sees Bobby as the bigger threat to Johnny. Yes, Bobby came in second to Johnny in the previous year's tournament, but it's not too much of a stretch to think that Bobby improved greatly and that Kreese knew he was a legitimate threat to beat Johnny this time around. Johnny was emotionally distracted because of his breakup with Ali (and Ali was now going out with the boy Johnny was going to fight in the finals), while Bobby was confident, calm, cool, and collected.
In season 2 of Cobra Kai, when Johnny reunites with his old Cobra Kai gang, Tommy reveals to Johnny that he actually had feelings of his own for Ali back in high school as well. He was going to ask her out, but Johnny "struck first". In retrospect, it explains certain behaviors Tommy exhibits here.
When Johnny and the others first show up at the beach, it's Tommy who notices Ali flirting with Daniel and points her out to Johnny. Bobby and the others are like "she’s ancient history" and "I thought they were done", but Tommy’s the one who brings Johnny’s attention to it and then supports him as he goes down to start a fight with Daniel. At one point, Tommy holds Ali back to keep her from interfering as Johnny beats up Daniel.
Tommy’s also the one who later sees Daniel having lunch with his mother and calls Johnny’s attention to it.
When Daniel walks up to Johnny's gang to mock them for being unable to harm him until the tournament, Tommy is bristling with as much rage as Johnny is, yelling, "Must be 'Take a Worm for a Walk' Week!"
At the tournament, he's the one to shout to Johnny "Get him a body bag! YEAH!" Dutch and Jimmy seem ambivalent and Bobby hates the idea of intentionally sabotaging Daniel.
Daniel and Ali having an encounter with Johnny towards the end of their first date at Golf 'n Stuff takes on a different light after Johnny mentions in the first season of Cobra Kai that he took all his first dates here in high school, and thus encourages Miguel to take Sam there.
, traditional Okinawan Karate such as Miyagi-Do did the same, leading to Daniel and the Cobra Kai pupils simply being stronger, faster, and having more stamina than their opponents. In addition, most schools have students who come and train for a few hours a week, whereas Daniel spends all day every day building stamina. And at least at first, it's quite possible that the Cobra Kai pupils were caught by surprise when Daniel proved himself their equal if not their better in terms of physical conditioning.