So maybe it wasn't done knowingly, Laguna?
Maybe Gleowine (who after composing Theoden's dirge apparently never composed another song), was not, ultimately, the author of the song which you're clinging to so fiercely? It's implied that he intends to, but he's old and world-weary, and very nearly drunk himself to death over something far less traumatic earlier in the story.
The song was written many years alter, by an unnamed poet.
The most sensible assumption to make from these facts is that Gleowine never finished composing the song, and that it was completed, or written from his notes and records, by someone else, many years later.
You can bang on all you like about warrior culture and the anathema of considering war-broken people as actually dead... it doesn't make you right. You've been very vocal about this, but not very accurate.
People are people, and none of them perfect. Gleowine is an old, old man, and he loves Horn dearly... and you can tell that it has more or less broken him, far more than the war and fighting itself, to see Horn so thoroughly destroyed by the battle. He is sentimental, and he is aching much in the same was as many others, and from the perspective of 'real people' I can fully see him feeling as though Horn, too, had been taken from him, and from everyone, regardless of his continued pulse. His culture may say differently, but people are people.
So it's perfectly feasible that he couldn't bear to leave Horn out of the song, even while knowing that, culturally speaking, he ought not put him in. I can fully see him never managing to complete the song as a result of that.
I can also fully see someone else picking up his notes years later, completing the song that we have, and thus including Horn's name as a result without knowing otherwise... especially when you consider that MOST of the individuals mentioned in the song are people of lordship, or other important standing... Even the red-heads are sons of a thane... but Horn, if it be OUR horn... is not.
your problem, Laguna, is that you're taking absolutely everything at absolute face value without thinking about it in the slightest... or at least you seem to be. You've taken at face value as absolute truth that the Song is accurate. It might not be, Tolkien himself is on record as noting that the histories an stories told by his characters are not necessarily accurate... but you don't seem to care about that, you want to treat it as absolute gospel. Just that same you've taken turbine's work of implication and suggestion, too, as statements of absolute definitive certainty, when they aren't, and thus treat them as contradictory, when they're not.
Back to the matter of Gothmog....
Aragorn's 'stern talking to' was a potent exercise of power. Please do not forget how powerful word and song are in Middle-Earth. Aragorn, by his lineage is capable of exercising very literal force of power and grace through his presence and his words... it's not just inspiring, it's tangible far more so than in our world. The oath-breakers that linger, if you recall, were cursed to that endless fate by simple words, spoken with power, by Aragorn's ancestor, and he shares that strength. In this particular case, reaching for his sword would have been the Lesser action of aggression against Gothmog. Consider also that, in those few moments, Aragorn knew that Halbarad was still alive, but not how badly harmed he was... he needed Gothmog and co. off the board as soon as he could, so he could check on him... and starting a brawl was NOT the way to do that. Aragorn was keeping his head in the face of a powerful enemy... are you suggesting he shouldn't have?
Personally, I WAS a bit disappointed with Golodir's end.... mainly because I was expecting that he and Gothmog would need to be the end of each other, ultimately. But, I'll be completely honest, I was pleased that he showed a bit of spryness at the end... there's been far too much trend of rangers being made a joke of, when they deserve more and better. Halbarad brought 35 rangers to Aragorn, and to the battle... and that 35 was an ARMY. They're not 'normal' men, not one of them, and throughout this game I've felt consistently that they deserved better treatment... so in the end, an old, tired, ranger, resigned to his death still going out by felling a battlefield champion gortherog in its prime... I'm ok with that.
Rider, Fighter, Virgin, Lover; Watcher, Chaser, Bearer of Pain.
Victim tormented, Abused and Broken; Rise from the ashes and Hunt once again.
And Vengeance Be Thy Oath.