For comedy side quests, Hildebrand tends to have a lot of foreshadowing and dark implications that pay off elsewhere later. The ARR quests show that primals just need strong emotion and a power source, foreshadowing Hraesvelgr's later reveals about their true nature, while also showing the dark history of Ul'dah that gets unraveled more in the Sil'dihn Subterrane variant dungeon in Endwalker. HW's Grand Sers demonstrate how some of Ishgard's traditionalists aren't so willing to give up the old glory days and are more than happy to keep killing dragons, which is not only a big problem in the post-HW quests, but also comes back again in Endwalker in the caster role quest. Stormblood is the main exception, since the main story hasn't really gone back to Doma, and we still don't know what happened to Gilgamesh.
And of course there's no Hildy in Shadowbringers, except for a rare cameo in the Heroes' Gauntlet that's mostly a callback to a wordplay joke in the ARR quests that didn't translate well. (There was a bald man who confused Warrior of Light (Hikari no Senshi) with Gentleman of Light (Hikari no Shinshi). Apparently Elidibus's summoning spell made the same mistake.)