Here is the problem with an abridged version:

1) It would take a lot of resources:
It isn't just cutting out quests. It requires checking and altering dialog, modifying cutscenes, checking and adapting story flow to insure important information buried among the filler isn't lost and then all the QA that would be involved. That requires developers working on it. That means developers not working on endgame content. To do this they would have to cut back on the patch content we receive.

2) It would be a very short term fix:
The MSQ isn't stopping anytime soon. What happens in an expansion's time when SB has been added to the MSQ? What about the expansion afterward? There is a lot less filler to cut from HW so the actual gains you get will be limited.

Clearly its an issue but cutting back on the existing story won't really work. The other suggested solution, unlinking the story from progression doesn't sit well with me simply because I strongly suspect that such a change will almost certainly impact the story in a way I would find negative, if not simply to the story then to immersion. It would make far more sense to just let people skip forward in the story if they don't want to do it. Let the stories structure remain how it is. Just give people the option to skip forward.