In my case, I have never identified with the cuck, and have never met anyone over on the doujin sites that identifies with them. Everyone I know over there seems to cheer for the cuck's downfall and mind break, me included.
Your comparison to revenge stories is a very fitting one though. Seeing the evil ex-party members who banished the protag get their just deserves does elicit similar feelings as a NTR story.
(Just to note, I use "you" as a general term not as in you specifically)
I'm starting to wonder if this sort of "person who enjoys ntr from the perspective of the person being cucked" is heavily exaggerated. In the first place, "cuck" is one of those loanwords from incel forums, similar to "mogging", "chad", "beta", etc. Not the original meaning, but the way most people use it: Someone who allows their partner to be taken with little to no resistance. Someone who was too weak to defend what was "theirs". It makes sense that the meaning is all over the place because it has lost the original, specific meaning, so now it's more like a feeling. It's an insult, not an identity.
Like how most ntr hentai ends, particularly doujins versus a longer running series; at least from what I've seen usually there is some kind of often absurd breaking point where the person getting cucked does the Napoleon "There's nothing we can do" meme and resigns himself to supporting his not-baby, says "alright I'm going to pretend I didn't see that" and ignores the "I'm sorry husbando he's just so good" moment that either just happened or will be continuing to happen for the rest of his marriage, or abandons his wife to be someone else's new wife or something. And I would have to read some hentai/normal manga that
do feature story arcs to better understand this (don't hold your breath I really feel apprehensive about going that far), but when it comes to cuckoldry in a real life sense, it's not about some guy coming in and having sex with your girlfriend without either you or possibly your girlfriend's consent. It's not about blackmail either.
It's about sexual humilation and shaming (and there are 100% a lot of people who are into it who are weird about it), but it's not about permanently losing your partner. I sort of question if, unless you were like on a deep level of unawareness about what it was doing to your mental health, why someone into someone they love having sex with someone in front of them while enjoying it and possibly telling them how much better they feel than him, would be down for sitting back and watching some guy who is barely in the story not notice his partner cheating on them until the last moment. Wouldn't they appreciate more of a "love conquers all" kind of thing? In fact, how many manga straight up end with the protagonist truly being left with nothing, like even if their partner cheats on them and leaves them they don't find someone else, they don't find fulfillment, they just are alone and unhappy?
Maybe we're looking at it from the wrong angle. Maybe the bull/sadists are the majority who consumes ntr and the cucks/masochists, if any, are the minority. At least in a doujin sense. Maybe some of what people consider "NTR" in manga is in fact but the author isn't writing it from the perspective of someone who
wants to lose their partner forever, they're writing it from the perspective of someone who values emotional bonds over physical bonds, or enjoys the fantasy of taking the heroine away from "the bull"
despite the pleasure the bull could give to the heroine sexually? Perhaps we're collectively too trapped in the incel framework of "Girl taken away so she is tainted forever". Might be a stretch but as I said previously I do not think I have ever personally met someone who said they enjoyed being cucked; Maybe a few people who liked watching people go at it but straight up getting demeaned? No not really, and I have been places where one would think you could run into them.