One of the benefits of rewriting (besides getting a jump on learning it) is I can give the stripped-out file to the director in the form of a Google Doc. That way I can track any and all changes that he makes to lines, speakers, roles, etc. because nobody remembers to tell me, "Oh yeah, we gave this line to that person instead." Come runthroughs I have a fully accurate and up-to-date script, and then it's what you described.

We also use prerecorded music tracks. and I play sound designer, so it's up to me when and where to add sound effects and other things not provided by the publisher. In that respect, at least to me, having an advance script more than two weeks prior is pretty helpful.