How long is the run? I didn't have any runs in school push too far past the two week part.
In a professional setting on a long run it's the SM's responsibility, you're correct and it's good that you realize and are eager for this. The primary reason behind this though is more logical than artistic - on two, three, four year run the director has gone off to his/her next project after opening night. In a collegiate setting the director is presumably still there as faculty, grad student, or some other role.
But, it is good practice for the SM to have experience with this before leaving undergrad - you are paying for the education and training.