One thing that bothers me about keeping a ship in the air while docked: If the balloon needs hot air to remain afloat (if it was filled with a light gas it wouldn't be able to sink and rise again)
This isn't true. Hybrid airships currently alter altitude by compressing lighter than air gas into tanks and allowing air back into the cavity. That being said, I'm sure the system works completely differently since it's super obvious that the balloons are filled with dark matter.
May see this touched upon in the VN. Prototype design I've been working in is there is a valve shutoff which seals the system. Keeps it afloat when docked.
If you look at some of the ship designs, it is clear they were never made to be flown without their balloons. Pyra alone should not be able to maintain it's structure without it. There is no framework that connects top to bottom other than the ladder and that isn't strong enough to hold up the armored bow.
Chaladon and Anglean I believe are the only two nations which utilize ships capable of water landings. Most traders would likely modify their ships with water landing capabilities if they expected to trade anywhere near a coast. Prototype design we're using in the VN takes this into account.
Spires I don't think are trading vessels. I think they're border defense or guard ships. The design is too slow and would require too much customization of docks. Makes more sense to me for them to be deployed around capital cities from their own custom berths. Trouble happens, all they'd have to do is fly up and start raining fire.