The 96% number refers to the orange fuel tank. Once you factor in the shuttle, the payload, and rocket engines, it's more like... 94% fuel. Some rockets are 88% fuel, but still only ~2-3% payload. A lighter rocket could mean 10% payload.
whose main problem is:
The simplest design has a pressurised water tank where the water is heated before launch, however, this gives a very low exhaust velocity since the high latent heat of vapourisation means that very little actual steam is produced and the exhaust consists mostly of water, or if high temperatures and pressures are used, then the tank is very heavy.
Although, that would also require the material to be very heat resistant as well. Which might be problematic. Compressed air might also work at that sort of level of material as well. At least for initial launch stages until you need to switch over to another type of propellant (or a more controllable engine).
I thought the Space Shuttle was already primarily a steam rocket. It held liquid oxygen and hydrogen, which was combined, ignited, and the result is high temperature water (steam).
Another way I wondered about, is to have a cold water tank with a nuclear reactor in it. As long as you ignore the safety part of the equation, do the physics work out? That is, would you get more thrust than from recombining hydrogen/oxygen?
The issue with rockets is that it takes x amount of fuel to get to your destination once in orbit and x amount of fuel to get the craft and the destination fuel to orbit.
It's why rockets generally work best in stages (you just drop the extra support structure needed for the fuel). It's really an exponential problem. Every lb of infrastructure you remove from the rocket makes it _much_ more practical.
See my comment above about having magic space elevator materials available anyway. Steam rockets and the like start to seem very practical at that point. And probably less insane than a cable all the way to space.
use it to make cheaper/lighter rockets.