Why did Freddy try to possess Jesse in this film instead of kill him? When he attacked in the first movie, he ended up getting dragged into the real world and got his ass handed to him by Nancy, no doubt bruising his ego and proving to him he was still vulnerable in the real world. He doesn't seem to have killed anyone since, so he's had years to sit on his defeat and sulk on it, unable to kill more Elm Street kids. Then Jesse's family move in, people totally unconnected to his death whom Freddy doesn't have the same lust for revenge towards. He is willing to try something new to get access to victims again and get more power in the real world - through Jesse.
Relatedly, why doesn't Freddy try possessing victims again (until Freddy vs. Jason, and even then it wasn't the focus) when he can use possession to not only kill more people without needing them to fall asleep but also bring his Reality Warper powers into the real world through a host body, protecting against his weakness of losing powers when he's forcibly dragged into the real world? Jesse, Lisa, and the earlier scene with Jesse's little sister Angela proved that the host can resist him and prevent him from killing people they care about, and can use this to defeat him again for who knows how long. Freddy's not just a kill-happy maniac but a sadistic kill-happy maniac, so the idea of not being able to use someone's body to force them to murder all their loved ones would be a huge disappointment. That it can be turned against him and used to defeat him again seems like an unnecessary risk to him when he can go back to the old formula and pick off teens just fine in their sleep, without any hosts to resist and only minimal risk of getting dragged out.