I think the Burn probably does make more sense as a dungeon. If it's so desolate, it's unlikely to have many of the things that you would expect on a field map - NPC population, functioning aetherytes, etc.
Though I suppose there's a chance we'd get some kind of habitable underground area that's visited separately to the 'dungeon' area?
(Also Azys Lla is such a weird place. That eerie sky that looks like we've ended up on another planet. It hardly feels like it's part of the same game.)
Well, "Alpha and Omega" were almost inevitably going to be set against each other at some point, I guess.
Though, if Alpha is part of Omega's computer simulation in the first place, what does that mean if we destroy Omega?
I agree with the rest of what you wrote - I missed a lot of the emotional impact of Ysayle's death because I was still thinking "wait, what, is that all the involvement she gets in the end?" - and then afterwards the story almost rushes onwards to the next thing, no time to mourn.
However, even though we "never found the body", I think there's no question of her (or Haurchefant) coming back because of the scene we get with them when we save Estinien. It's a farewell and closure, an assurance that they are at peace and 'moving on'.
An aside to this - I really wish the 'ending scenes' of Heavensward, particularly the placing Haurchefant's shield at his grave, happened at the conclusion of Dragonsong instead. There was a symbolism of carrying the shield with us - carrying him with us - and I feel like we should have kept it until the very end. (Also the actual credits rolling, at the point when things were unresolved and we'd just seen Estinien taken over by Nidhogg, felt like I hadn't properly earned it yet.)