Is there a direct Torah-prohibition to put yourself into (unnecessary) physical danger?
Yes there is. It says in Deuteronomy 4-15 “and watch your life very carefully..”. There is also a siman in Shulchan Aruch (Y:D 116) about not doing different things that are dangerous. In fact almost all mitzvos are pushed aside in a life threatening situation, for example, a person may eat non kosher food, or desecrate the Sabbath if it is needed for to keep a sick person alive. Life is one of the highest values in the torah, because without it, we cannot do the service of H-shem, and because H-shem put us in this world in order to live.