Do pyromancers do anything other than make and store wildfire? If the monarch is not interested in burning people, or has a dragon for that, what else can they do?

Well, they’re alchemists, so I would imagine they’d be working on transmuting base metals into gold and silver or finding the universal solvent , trying to find the elixir of youth or the panacea, and other such worthy endeavors. 

If they’re anything like historical alchemists, however, I’m guessing their practical utility would be in proto-chemistry.