It's entirely possible that a person can be the best in everything, but not really as it is now. as you imply, Hydaelyn does come across as a Mary Sue in the current lore. She was in the seat of The Traveler; one which invites world-class good guys by its' nature, so it would make sense for her to be "the best at everything and well-loved." the obvious example of the premise working is your character, the sundered version of The Traveler, the Warrior of Light, being well-loved for good reason and the most powerful and nobody bats an eye; clearly the problem is not in premise but execution. unfortunately, it's poorly communicated in-game and she comes across as a doofus. For example, if Hydaelyn did actually do everything correctly and was good 100% of the time, while also making personal sacrifices (as the story wants us to believe but doesn't show beyond a cutscene that implies it), it would make sense that she was loved for the reasons the cast does. For now, the story in EW feels like 2 entirely unrelated expansions cut together because it was the 10-year anniversary and they didn't want to wait until the 12th for the big finale, which meant they had to fanangle all of the important and meaningful character arcs.
I feel like something that could have fixed her EW character is even a short quest that shows her fear about the job required as well as an actual attempt to change the future, instead of her immediately going "well I'm going to play by the rules of two immensely homicidal maniacs because lol." it would establish her as a well-meaning but imperfect character, and failing to convince the convocation about the final days would make a great failure point to allow for her becoming Hydaelyn as a last-ditch attempt to save the universe.
and a minor side note: the ea (blob aliens) could have easily circumvented entropy forever by time-traveling backward, as we know it's possible and only uses the aether of the future. at least a mention of them trying would be immeasurably better than not for purposes of storytelling, as primals seemingly do not require actual knowledge of how to do something in order to do it, and a severely weakened Garlond Ironworks only took a few generations to figure it out. Honestly, the addition of entropy in my fantasy universe literally killed any sense of magic the game had.