I just think its interesting how at the very end of the story, we see Merlin walking past Avalon, the place where he sent off Arthur all those centuries ago. There are many different ways the scene could've went on to display his everlasting loyalty. It easily could've been a scene where maybe Merlin was with his wife and a kid who was named after Arthur, or he became a historian/scholar who kept the Arthurian legends alive after everything he went through or maybe even a physicist trying to build a time machine, find a loop in time to go back and fix the past.
But no.
We see him all alone, old and unequivocally miserable. No longer meddling with fate nor trying anything at all. Lost in a world beyond time that no man should live past or would even be able to comprehend. We see that he never moved on from Arthur, having somewhat a glimmer of hope deep within him. Nobody speaks about how insanely difficult it must have been to have hope especially when you have no end to your own life. As mortals, we can't even bear grief for a short period of time. Yet, Merlin lived the cursed life of an immortal, a life where he will only keep losing everyone he's ever loved. A life full of grief.
In the modern world shown, nobody even believes in magic or practises it and yet he...still believes that someday Arthur will return to him. In the past, he reiterates that he just wants Arthur to see that everything he does is for him. He tells Hunith that Arthur only likes him because he doesn't know him. We see he acknowledges that Arthur is doing acts of service because he likes him yet Merlin couldn't be satiated because he still wasn't his true self to Arthur. To be seen and known for who you truly are is to be loved, that is all he ever wanted from Arthur, even from the very beginning of their relationship.
"You never once sought any credit"
"Its not why I do it"
During the magic reveal, he said "I use it for you, Arthur. Only for you.", still desperately wanting it to be known that his entire life was devoted to Arthur. There was no talk about legalising magic and whatnot between them either after that. He only kept repeating that he was born to serve Arthur. We see in real time just how much he meant when he said "There will never be another like you, Arthur." Evidently, he meant that Arthur is the Once and Future King but it also plays out for Merlin, because there never was anyone like Arthur in his life after that. To the point where he could find no purpose upon losing Arthur.
And yes he keeps saying that its his destiny to be Arthur's servant, that he grew up and learned the meaning of duty but is that really all it is? Towards the end, it was apparent that Merlin's objective was no longer for magic to be accepted in Camelot (as much as he wanted it). Ever since he found out about Arthur's Bane, it was all about keeping him alive. Even when the great dragon told him that there is nothing he could do anymore, Merlin could not accept to lose Arthur. "I can't lose him, he's my friend." It didn't matter that magic isn't legal yet in Camelot. He could not give two fucks about it anymore or else we would've seen magic in the future scene. One can assume that he completely stopped trying to find a solution. Or even lost the will to live.
What I'm trying to say is that, the final scene really is more than just an epilogue to show his loyalty, immortality and despair. If you think about it for a moment, it shows that somewhere along all the fights, snide remarks, banter, and what he and Arthur think isn't exactly a friendship, - they're stupid, don't mind that - he was in love with Arthur. And Arthur loved him in return even in the face of death as the truth came crumbling down. Its not as simple as 'falling in love' because, I don't think Merlin woke up one day and realised that he was inconveniently in love with the idiot arrogant prince who was tied to him by fate.
Their love was inevitable but it definitely stopped becoming destiny and duty a long time ago, it became a choice. "I'm happy to be your servant till the day I die". Merlin was, and I quote "putting up" with Arthur not because it was his life sentence to do so; it was because he wanted to. The worst thing of all is: Merlin chose to do it for the rest of his life.