I'm not sure if you yourself were intending the "new prince of Dorne" who had a single line as being inherently a negative thing in your post, but I've stumbled on a few examples online of people really complaining about that and saying it's "such shit writing" because this guy wasn't thoroughly explained and didn't have much to do even though he was included. But I think actually that's what was needed - more "new Prince of Dorne"s. Ok, not exactly, but if we accept that the story has to stop expanding somewhere and that the screentime is going to be devoted to the major characters and factions, then the only way to preserve the feeling of the bigger world is to include references or brief appearances of characters and factions that won't be given significant screentime. I don't need to hear the show's attempt to explain who the new Prince of Dorne is (especially since after the Sands took over Dorne the ship had already sailed on robust politics in that region). But we learn he exists, and he's still antagonistic to Cersei - that info is better than never hearing mention of Dorne at all. I'd have been happy to get a little bit of that for some of the other regions and the rest of King's Landing.
Of course, seeing that something like mentioning a new prince of Dorne without elaborating is classed as Bad WritingTM and the many reactions of "So ___ or ____ was pointless then?" (I usually find those sorts of statements quite bizarre, but I'd probably write a whole posts worth if I got into that) I can see it'd be quite a fine line to tread for the writers to try to put in a bit of extra texture if the characters or things mentioned aren't going to be immediately important to the scenes. Doubtless it wouldn't have pleased many people, I'd have liked it though and feel it would do a bit to ease the difference between the feel of the earlier seasons and the last few.
I had problems with the new prince of Dorne because Dorne was one of the biggest balls dropped in the series. It's not their fault, let's just get that out of the way - in the books Dorne will likely have an important storyline that's been cut from the show completely, so they had to try and preserve the cool parts while cutting out the parts that would make sense for the book storyline later, and the result was a bit of a mess. Having said that, just mentioning "the new Prince of Dorne" kinda just... reminded people that the show has had narrative issues for a while. I think it would have taken one phonecall from their people to GRRM's people (like his fact checkers Elio and Linda who worked on his encyclopedia books) to ask, out of the Sands and minor lords who were still alive or not mentioned in the show, which is the most likely candidate to rule by the time of the show? And then they could have just put that name in.
It's just one of those small details that the show, up to now, loved to highlight. Remember even recently, in the Tower of Joy scene, when Ned carried Dawn up to Lyanna's bed so that Jon was "born under a bleeding star"? Loved that shit. Give me more of that. If you have time for 20 Varys has no dick jokes, you have time to name the Prince of Dorne.
I don't have problems with "arcs going nowhere" or people being "useless", sometimes that's just how the dice lands in ASOIAF. As long as you show characters trying
and failing. Or if you leave the useless character out of the scene at all. Yes, we all love Arya, but she is the least interesting person that can witness the chaos in King's Landing. Could have been Jon, could have been Davos, could have been an unnamed Dothraki fighting not to get literally killed by his own commander. Anything that plays into a theme or has any emotional significance at all.
One of my favorite "arcs" in the books is the epitome of a "useless" arc - the one of Prince Quentyn Martell. The kind that makes you go "what the hell was that all about". He goes off into an adventure, we follow it in full gory detail, we meet him and learn his hopes and dreams, we learn he is on a mission because of his powerful father. He gives all he's got, goes through hell, even though he is unwilling, he walks into disaster. He goes to propose a marriage pact to Daenerys, even reaches her, gets rejected, and... well. Let's just say his story ends in the most unceremonious way possible. What was the point of that! Well, Dorne is a natural and powerful ally to Daenerys, and she needs to be without allies when she arrives to Westeros for the story to work, so Martin has to figure out a way why this natural alliance would fail. But also, it plays into all the bigger themes of the books. Life is not a song. It takes so much to make it, and most of us are just people, even nobles and royals. Don't bite off more than you can chew. You should have stayed home. Martin relishes in writing this seemingly useless story, the writing is so vivid, so powerful. And he makes me love it.
I wish Jon could have had just one or two conversations that played into these themes. He's Arrived, he's traumatized, they told him his entire life was a lie, he fought the dead and barely survived, the Red Priestess who revived him goes and he's still alive. All he wants is to serve Dany, because that is his duty, to the bitter end. All he wants is to tell his sisters that their father wasn't dishonorable. He tells them. THEY REACT, WE SEE THEIR REACTION. Why do we get all these Stark moments with the meaning cut off?? One of them schemes against the queen he swore to protect. He is the only one who can get near enough to kill her after she breaks bad. He is a kinslayer, and a queenslayer, all in one. In all this emotional turmoil, where the only thing he's useful for - the thing he must have been revived for, because the show believes in destiny - is the thing he least wants to do in the entire universe, we get maybe two lines from him, and the nature of his tragic act is completely flattened, because:
it barely registered because after Dany nukes a surrended city and is framed with the wings of the dragon behind her to make her look like a demon and all of a sudden makes nazi rethoric about "freeing the entire world", what else can happen but her killing? you can find a gazillion comments both positive and negative about the finale, but I bet there won't be basically any about "Jon should have totally not killed Dany".
Basically one throwaway Dorne prince gets me more emotional in the most bloated ASOIAF book to date than Jon, the literal song of ice and fire, makes me in the finale of the story I have waited 13 years to see.