The Current Lunar boss requires a couple of things be completed before given a chance to fight it.
1. Find Pearl's island and complete her demands to increase her happiness. (May take several seasons)
2. Explore the Caves and uncover the Ancient Archives. (May take a few days)
3. Complete the lunar event and obtain a iridescent gem. (May take more than 1 season)
4. Defeat Crab King, a very resource intensive fight.(May take more than 1 season)
5. Transport and place all three altars. (May take several days)
6. Complete Wagstaff's event. (May take a few days)
7. You still have to fight and defeat the Champion.
Here is a couple of points to help the discussion:
We know Crab King has lore connections to the moon overlords, but given how pearl's quests unfold, is it thematically appropriate? (His fight does not contain moon elements, the moon stuff occurs in the background. His and pearls quest mostly revolves around their relationship)
Given Crab King's drops, does obtaining the pearl feel unrewarding?
Given the length it takes to obtain Pearl's pearl, would it be more appropriate to just take the pearl out of the equation?
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Personally, I think it makes sense to have Crab King drop the tribute without the need of Pearl's pearl. The pearl is a symbol of their relationship and should be up to the player if they want to explore what occurred in that relationship. Gating content behind a story arc/side mission can work if done correctly but Pearl's quests are just a series of menial tasks. You get a couple of strings of texts and due to the lack of story telling elements in the game, it gets repetitive. I believe this is a nice middle ground for everyone involved.