We have no idea if we'll get an applicable trait for the Temple nor if we'll get any more discounts on AP needed, so even if it gets unlocked we'd likely need two turns to do so, giving us some free AP to spend on other things.
For the Cure, in no particular order:
a) to spite the Druchii
b) it might be a good path to get Vardanis a familiar
c) it's important to Vardanis personally, and has been an ongoing plot since before he came back to Chrace from Saphery
d) it soothes our Focus
e) it just seems like an action that's both interesting and good to do
We made a Tier 3 for the Phoenix King without Bits and Bobs. At a guess it's more of a way of finding cool one-use materials we can use to supercharge a particular item when crafting. It could be useful for the Loremaster Blade, but it'll by no means be necessary.