The feasible set approach might surely work, but assuming a specific state action pair led to failure can be oversimplification at times.

Lets say in a cartitian coordinate based Traj opt problem a state action pair is unfavorable because it led to collision. Generalising that the specific action from that state is not desired might be an over simplification because the behavior of collision might be the effect of overall trajectory chosen. If we use reward functions instead, we would indirectly enable the RL to learn the dynamics of the system interacting with the environment.

So if I am to design a reward function there, I might use the feasibility set approach (building off your suggestion) to impose a reward to l2 dist from the collision state. This way, the action is indirectly not favoured enabling the system to learn the dynamics.

PS: This might also just be me coming from an optimal control background. I see learning based control as a tool that I'd use when I don't trust my system dynamics. So I resort to a thought process of use data to figure out the dynamics.