For rigid bodies, all the particles can have different linear velocities but the same angular velocity, so it makes it convenient to talk about the angular velocity instead. From there, we get to ideas like angular momentum and torque, which work the same way for angular motion as momentum and force do for linear motion.
However, if we have a system of $n$ particles freely moving around, say a gas, do we still use these ideas? In that case, the moment of inertia is constantly changing.
If we apply a constant force to any of the particles, then it'll result in a non-constant torque because of the continuously changing position vector. In case of rigid bodies, this is not the case because, in at least the 'axis of rotation frame', the torque due to a constant force on a particle is constant because the angle between the force and the position vector of the particle remains constant because of the rigid nature of the body.
For non-rigid bodies, there is no 'axis of rotation' frame, so torque is also very inconvenient to talk about.
So are these ideas only used for motions where the whole system can be ascribed the same angular velocity at all times?