One of the things I love about Norrington as a character is that he was originally written to be such a stereotypically selfish asshole threat to Jack and Will's lives and Elizabeth's happiness, but they realized something better could be done. He almost was a more obvious incarnation of an almost mustache-twisting villain, wanting to trounce all pirates for the sake of conquest and wanting to marry Elizabeth purely for the power it gains him. And they changed that ultimately, which I've always been grateful for, because it's a choice that elevates a surprising amount of CotBP's subplots.
But when they made that change, they didn't just throw it all out. Instead they still kept a decent amount of the bones of that antagonist's writing and simply ... nudged it (especially the performance) in a slightly different direction. The result adds a fun layers of humor and nuance to him and every relationship affected by him. To me, it's always added to his appeal as a character.
His final, canon portrayal still is an antagonist who pursues power and glory, deals out the death penalty too zealously, and gets in the way of the desires and goals of Elizabeth, Will, and Jack. (And obviously has a very fundamentally different world view than the protagonist and her supporting leads as a part of that.) The difference is that he is not motivated by avarice but something more like chivalry. He doesn't pursue what he does out of a malicious desire for conquest, but a earnest desire for Order, a belief that he serves a greater good for society, and genuine soft spot for Elizabeth. And he just also happens to like feeling like he's the Best Guy for the job while he's at it.
And I don't know, watching that interplay in him just makes him a funnier character over time in CotBP and DMC in particular. Like he's straight up full of himself in CotBP. Sorry if that feels mean to say, but overlooking that is kind of a disservice to the character, in my opinion--especially because his greatest downfalls ultimately hinge on acts of hubris more than anything else. He obviously LOVES his job, and most specifically love the position he's earned. He seems to enjoy the chances it gives him to show how Great he is in front of his men. Like I just know in my bones he was absolutely relishing the chance to throw back that "almost escaped" line at Jack, reciting it in his head--and he does that stuff all the time.
Ironically, I think that makes him a very interesting mirror to hold up to Jack and Will, especially with Jack's fixation he also has about his captaincy and its notoriety and Will's desire for recognition for his own work.
It also makes Norrington's proposal to Elizabeth more comically ridiculous the more I watch it over the years, especially when paired with her later scene with Estrella on how it was The Worst Thing about her day. Because even if he's performed to be sweet and bumbling, really the moment is written to be so deeply about him in his mind.
The way our girl is visibly and audibly suffering, and he doesn't notice until she says out loud "I can't breathe" and then still somehow thinks that it's about him. He even says she "looks lovely" but doesn't SEE how she doesn't FEEL lovely? The way that his reasons for proposing to her (while looking at the horizon instead of her, mind you), "I have a To-Do List for my life, and the next item requires a Fine Woman--how convenient that you match that description!"
I don't believe that he's being willfully uncaring by a longshot, but holy shit, my guy... Instead The way he goes about it, makes it come across like he's proposing to his career with Elizabeth as the ring, instead of the other way around. We're really not going to focus on her at all in any possible way? Not a word about why she, as Elizabeth Swann the individual, is the one he hopes to marry? Just "This serves my goals! I'm so nervous!" Even if she were not in a corset at the time, it would still be awkward and kind of insulting to listen to, especially because she already is Not Interested. The fact that he doesn't not notice she's literally in physical distress is just the painful cherry on top.
But! All of that is true AND it is also true that he was initially willing to jump in the water after her, that he cared enough about her romantic feelings to not force her into an unhappy marriage, that he thinks he's making the world a better place with all that he does. The combination of those things are what have made him Him.
Anyway. Norrington is still an antagonist even if he doesn't "feel" like one. That's something that adds some fun complexity to the trilogy's story in places that could have been by the numbers like DMTNT was. That's all.