Why does the god of the sun or the moon care about healing?
Because they care about their followers being alive?

For the same reasons, one could think all gods care about their clerics being able to survive a fight, or being prepared to defeat the religion's enemies. So all the gods might give their followers a serie of spells that are combat focused: Flame Strike, for example. The cleric of Roads and Merchants give it to their clerics, so the clerics can smite bandits with them, while Corellon Larethian give it to their clerics so they can defeat Gruumsh's followers. And Heronious and Hextor give it to their followers for opposite reasons.
Hey, even those clerics can use that Flame Strike to blast away the abomination that a vampire is!.
However, each god might also give their clerics some *special* powers or spells which are focused in things that *do matter* the god's portfolio. Elhona might give their followers a Control Weather spell, while Pelor gives them Turn Undead.