I don't project what I believe Luke *should* become as a character. That's putting writers in a box. I look to see if his new actions are consistent with the Luke from the past, and in this case, they are. Rian also clearly understood the original Luke archetype (King Arthur) and applied it to his character. He didn't only focus on the positive aspects of OT Luke's character; he circled around the negative aspects of OT Luke's character, those characteristics that left him on that island in TFA (emotional, rash, unfocused). Luke is ascending to the rank of a master, can an emotional failure along the way lead to a crisis of faith? Sure, same as King Arthur.
So I'm not ignoring your point, I'm just disagreeing with it. Luke is still a rash and emotional individual. He displays these characteristics in ROTJ, especially when it comes to dealing with his *family*. When Vader threatened his sister, Luke goes into an emotional rage. All that calm, focused Jedi training goes out the window and he nearly kills his father. When he acts rashly, turns Ben into Kylo Ren, losing his sister's son to the Dark Side and leading to the death of his students, he becomes despondent and undergoes a crisis of faith and believes the Jedi must end. This situation was his fault, he let everyone down, his own family, the galaxy at large. And when he reviews the history of the Jedi, he sees Jedi were responsible for the creation of Darth Vader, full of pride and hubris, allowed Sidious to rise and destroy the peace of the galaxy. Rey points out that Luke was acting in error and emotionally and thought that Ben's final choice was made. Yoda said the same. It fits with Luke's negative characteristics which we saw in the previous films. This is who the character is. And this Luke undergoes a crisis of faith, completely making sense when you consider who he is (rash) and who was involved (family).
I'm not sure what your point about Leia only sensing Han's death just as he died, but this wouldn't apply to Luke. Luke knew his friends were in trouble in ESB before the Falcon ever landed on Bespin. It's not so much about sensing death, but friends in danger that set off visions in Luke's head and called him into action. So when JJ decided not to have Luke respond to that danger, it meant that something was seriously wrong with Luke, something that would require a great deal of explanation and nothing as simple as "it won't help enough" will do.
This "extremely strong urge to murder his nephew" was described by Luke as "a briefest moment of pure instinct...that passed like a fleeting shadow." Here one second, gone the next. Luke immediately changed his mind, within a second.
Should Luke have gone after Kylo and tried to bring him back? Sure why not? Rian could have easily written a line of dialog that says "And I tried to go after him, I reached out to him, in person and through the Force, but he was already gone." Would that have satisfied the people who didn't like TLJ Luke? Highly doubtful because they would not accept a crisis of faith Luke by any measure. They wanted optimistic, hopeful Luke.