In my opinion, you shouldn't be so dismissive of the world's reaction and the role the public plays in Superman's death narrative. He is a public superhero unlike Daredevil. When analyzing and reacting to Superman you have to consider the micro (the personal) and the macro (the public or bigger picture). The story of Superman and Batman's conflict and its resolution is what happened with Superman's relationship with the public in microcosm. Just as Danny Rand is the one most affected by Matt Murdock's death, Bruce Wayne is most affected by Clark Kent's -- except the whole world is in the same place as Bruce. They had been uncertain and untrusting of Superman, but they saw his humanity in his ability to bleed and to die, and they felt loved and believed in because he was willing to make that sacrifice for them. The whole world can't speak in individual scenes, but they can try to honor Superman as a soldier at Arlington or with a candlelight vigil in Metropolis. Headlines in The Daily Planet speak of a world in mourning. Among the faces of the mourners are ones who have been with Superman along the way like Pete, Father Leone, Perry, Jenny, Swanwick, and Farris. His loss and his inspiration transcends the personal, and that is important.
What's also important is the nature of the hero's death. Despite some of the dialogue in The Defenders, Matt Murdock didn't sacrifice himself for the city he loved. He sacrificed himself for the woman he loved: Elektra. He didn't need to stay with her and could have left with the others. He wasn't needed to stay with Elektra to save the city. He didn't leave with the others and put himself in harm's way for the greater good. By contrast, Clark sacrificed himself TWICE for the entire world. First, he took a nuclear blast in the hopes it would destroy Doomsday, and then he stabbed him in the heart. His final words were an expression of his love for Earth and for Lois. His death is framed, once again, as having both micro and macro dimensions, and it is presented as explicitly an altruistic act.
I also think you're not only overstating the way Daredevil's death was explored in its aftermath, but also splitting hairs by not acknowledging the specifics of what did or did not happen with the Defenders versus the Trinity or Justice League. Your interpretation of The Defenders as being more intimate and personal with individuals verbalizing their reactions is not reflected in the actual events or dialogue, for example. Before delving into the heroes, it should be acknowledged that in terms of personal connections, Matt's with Karen, Foggy, and Claire were less intimate than Clark's with Martha and Lois, but both Martha and Lois and Foggy and Karen had scenes showing them in mourning. We also got to actually see Clark's funeral, however.
Looking at just the heroes, Matt asking Danny to protect the city may have been more direct than what Superman did with Batman, but it actually isn't as personal. There is no reason for Matt to choose Danny for that particular message, and the truth seems to be that it wasn't his intention to inspire Danny directly. In fact, the way it plays out, Danny delivers the message to everyone outside of the collapsing building, telling those assembled, "Matt said something before he told us to leave. He said, 'Protect my city'." Since Danny's original Iron Fist destiny of defeating The Hand had been fulfilled, and after Luke Cage's sage advice about doing something with his privilege, Danny chooses to walk through the door that Matt's words had opened. He has a change of heart from someone who was focused on his own journey and his own mission to someone ready to look outward. Bruce is the same.
The words that meant the most to Bruce -- his rallying cry -- wasn't "Protect my city," but "Save Martha." When Clark trusted Bruce to save Martha, he was not only helping Bruce to access the best part of himself, but to feel re-inspired to dedicate himself to that purpose and to hope rather than stay lost in his trauma, fear, and anger. Bruce, like Danny, has the most explicit dialogue explaining how he's been inspired. For Bruce, he doesn't want to fail Clark again, so he will believe in himself, humanity, and in heroes again. He will recruit them and, as James Gordon says, return to cooperating with others.
As for the rest, Luke Cage and Jessica Jones are never shown to explicitly mourn Matt or to be inspired by him. Trish, Jessica's friend, tells Jessica, "Think of all the lives you saved." To which Jessica responds, "And the one we lost." That is literally it when it comes to Jessica's point of view on Matt. It's the same point of view we get from Luke when he tells Foggy, "Mr. Nelson, I'm sorry for your loss." Foggy has to be the one to tell Luke "It's all of our loss." In short, Jessica's and Luke's alleged intimate and personal verbalization of grief, inspiration, and reaction to Matt's death amounts to just them acknowledging that he died and to Luke not even viewing Matt's loss as a personal one for him. Now Jessica does decide to reopen Alias Investigations, but that isn't directly tied to Matt. She had already been investigating the architect, which is how she got involved in the war against The Hand in the first place, and since she never credits Matt, one can't assume that it was just him but rather the whole experience, including getting closure with Luke that inspired her to continue.
You could say the same thing for Diana in Wonder Woman. She ends her film in a return to the present day with a voiceover that informs us that she had stepped away to let humanity choose its own fate, but that now she embraces her role as protector. We know that it was Snyder's intention with both Wonder Woman and with Justice League to show that Diana was inspired by Superman whose death not only reminded her of Steve's but who helped resolve a core conflict of hers: the relationship between gods and humanity. So, unlike Daredevil's death, Superman's death saves the world from destruction, and it creates a paradigm shift so that superheroes can operate in public for the greater good. In addition, more insight into Diana's, Bruce's, the rest of the league's, and the world's reaction to Superman's death hasn't been seen yet; there is more to come. Thus, it's unfair to judge a complete story like the one in The Defenders against an incomplete one like the DCEU's.
