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 tempe

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?