I think Scott Manley focusses to much on the wrong aspects, water rockets are indeed cheap to manufacture and can be very safe. Steam boilers heated by fire will have an uneven temperature distribution, suffer from corrosion and have a much more complicated structure, they are not comparable. A steam rocket could be made as a single peace aluminum bottle, which would be extremely cheap and safe. For mechanical reasons, a ball shape or several ball shaped fessels in a line would be better than a cylindrical shape and could safe a lot of weight.
Heating could be done in many ways, with electrical heating being the simplest solution. The whole heating system can be attached to the ground, to keep the Rockets as lightweight and simple as possible.
Air resistance is important for rockets, and a rocket shaped like a flying carpet isn’t very efficient in this regard. I don’t think it makes sense to use so many small rockets instead of fewer bigger ones. With using only few large booster rockets, it might be possible to built an isolating fairing around them which is attached to the ground, not the rocket. The top of the fairing should be open, so that the rocket could leave the fairing during the start.
There was a group of students in Berlin (
http://www.aquarius-aerospace.de/) which developed water rockets, one of them wrote an extremely good Diplomarbeit (equivalent for Master thesis) about the potential of hot water rockets which I found somewhere in the internet. He became a professor by the way.
Unfortunately I forgot the theoretical maximum height of a two stage system, but I remember it was quite impressive.
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