> Optimization is such a rich field and should be of interest to any computer scientist who would describe themselves as "interested in solving hard problems" rather than just applying a well known technique to a specific class of hard problems.

Yes, but even if you are only interested in pragmatically solving problems, off-the-shelf solvers for various optimisation problems are a great toolkit to bring to bear.

Reformulating your specific problem as eg a mixed integer linear programming problem can often give you a quick baseline of performance. Similar for SMT. It also teaches you not to be afraid of NP. And it teaches you a valuable lesson in separation of specification (= your formulation of the problem) and how to compute the solution (= whatever the solver does), which can be applicable in other domains, too.