Even very high-order Runge-Kutta solvers may fail to preserve simple qualitative properties such as having a linear oscillator stay in its phase space. Meaning: simulations of physical systems will typically diverge unless you're very lucky. Might mean a satellite failing to enter stable orbit. Solvers for systems with certain specific phase space properties may be found (for satellites there are particular solvers), but do you always know beforehand what you're dealing with?
This "numerical power will solve every problem" attitude is bound to lead us to disaster. But then, so was the "ORM will solve every problem" attitude, for example. Luckily we have people actively researching symbolic computation. Jeez, without symbolic computation finding very high-order Runge-Kutta methods is exceedingly hard and error-prone.