I spent my career in electronic design automation, where practically every interesting problem is NP-hard, but we have to solve them, or approximately solve them at least, and because real-life problems often have structure, with the right approach very large problems can be solved exactly despite the theoretical complexity, and when exact solutions can't be found a decent bound can often be found that is an acceptable solution.

Sales people still have to plan their trips even though finding the optimal solution is NP-hard (to give one example). No matter; there are decent heuristic methods.