A Solar could spend his limited time feeding the hungry, curing the sick, and building walls around a city to keep out barbarians, and walls around Creation, later, possibly made out of the Neverborn. If he personally feels despair…maybe that Lunar with the really long legs she uses to crush him every other night can turn that frown upside down. Given that Gaia is immortal and the Shining Answer may not exist, or may not even be relevant to humans*, or could actively be a bad thing for humans**, a Solar might squander his Exaltation using his power to try to find it, when there are so many other pressing matters at home—things he really can deal with on his own, through his own power. For the people of Creation, you see, he is the Shining Answer.
* & ** statements are not meant to be canonical facts, only canonical suggestions ^^