This is a soft question. I'm not sure if it is appropriate for this site. Would someone who is only interested in string theory benefit from working out the problems in Jackson electrodynamics? I have to decide if I should take a graduate course in electrodynamics that uses Jackson. Would that be a waste of time? I think that it would be most suitable to engineers but I'm not sure. Do you think that an undergraduate course would be sufficient? I'm going to specialize in Theoretical high energy physics.
I don't think you can really properly graduate physics without studying Jackson (or equivalent). Classical Electrodynamics is not "only for engineers", but a basic prerequisite for almost every other branch of physics.
For instance, how can you properly understand field theory, when you've never seen Maxwell's equations in their non-tensor form? How well would you understand the concept of a propagator without first seeing how to use a Green's function? Sure you can study string theory without knowing anything about practically anything else (with is I suspect, one of the field's attractions), but you'd end up with an awfully poor education.