Why standard control tools fall short
Many classic control techniques, including the kind of feedback loops covered in general control theory, assume the system is fully actuated, or treat each degree of freedom as though it can be commanded independently. Applied directly to an underactuated system, these methods can fail outright, because there's no way to independently command a degree of freedom that has no actuator of its own. The controller instead has to account for how actuated and unactuated degrees of freedom are coupled through the system's equations of motion.
This coupling is exactly what makes underactuated systems harder to analyze but also, in a sense, more interesting: the unactuated part of the system is never fully free, its behavior is always shaped by what happens to the actuated part, and a good controller exploits that link rather than treating it as an obstacle.