In this parallel RLC circuit, why is there no current flowing through the ideal RLC elements until after the switch is open?
There is no mathematical reason why the current through the inductor should be zero. 

An ideal inductor with an ideal (zero resistance and zero inductance) closed switch across it will continue to conduct the same current forever, be that zero or 1000A. The current through the switch would be the inductor current added to Is.  

Most real inductors will have a current that quickly drops to zero because they have internal resistance. In this case, you have to assume some initial conditions, so inductor current = 0 is reasonable, unless you're dealing with superconductors, in which case it might be wrong.