"Because Peter Jackson inserted a kind-of similar scene for the sake of drama" doesn't really amount to a very robust defense of the characterization choices for Gil-galad and Galadriel.
I think that, fundamentally, making any Elf a POV character is going to be problematic. As soon as you compromise their Other-ness, you lose something of their mystique and grandeur. I also think the Dwarves suffer the same problem, albeit to a lesser degree.
I would have much preferred to see human stories with original characters set across the whole of the Second Age, with more of a standalone episode format, with each season focusing on a different period during that time. The great Elven figures (Gil-galad, Elrond and Celebrian, Celebrimbor, Cirdan, Galadriel and Celeborn) could have remained recurring touchstones, but would have remained somewhat aloof, adding emphasis to their immortality and giving room to explore this contrast with the shorter-lived races.