It's got me wondering about the other quests. Jane was supposed to restore life to her planet, which kinda happened when she went trickster... But maybe that didn't count due to the nature of trickster mode. Or maybe it just didn't matter. Or maybe she just didn't pick up her quest reward from her denizen!
Rose specifically ignored her quest in LOLAR, but it was probably the fact that Cetus ate all the fish. Not sure how the seer of light would fix that... Maybe convincing Cetus that returning the fish to the ocean would let their population grow, resulting in more food long term. I wonder what sort of end-game reward would have come of that, but AFAIK even doomed Rose didn't complete the quest. Unless the quest was to get really drunk with Cetus or something, allowing alpha Rose a better connection with the void and its horrorterrors. Just guessing aloud.
Kanaya says Jade needs to warm up the unnaturally LOFAF by reheating the forge. Presumably the planet's temperature is due to Echidna, which would fit with John and Rose's quests. Dave and her fix this by reactivating the Forge volcano (somehow). Doing this was probably necessary to forage the frogs and build the new universe, which is a reasonably grand denizen quest reward. Jade also visited Echidna later to get the quill for the scratch, but that probably wasn't her planet's quest.
The wiki doesn't even have a guess as to what problem Hephaestus may have caused on LOHAC. LOHAC has no problems and is basically the awesomest planet in every way. But Hephaestus does demand access to the Forge, so that he can fix something. That could be Dave's denizen quest, particularly since it results in repairing the Deringer into Caledflwch, the sword that can harm Lord English.