So this is something that annoys me as long as I've been an active member of SE. But at the same time I wouldn't suggest something as drastic as getting rid of the "Home" page all together.
I think the Home page does have some merit, especially for the new and casual users. It explicitly filters out garbage (post with extremely negative scores), and displays questions based on your tag preferences.
At the same time more experienced users have little need for those features. Users that care to moderate their sites do want to see the bad posts and take care of them by either bringing them up to standard or by closing/deleting them. Subject matter experts at the same time mostly use tag filters to look for questions they can answer, so they also have very little need for the Home page.
Now what I would find interesting to know is how many people actively visit a question from either the Home page or the Questions page, and if and how that correlates with a users reputation or their overall time actively spend on the site. My hypotheses would be that the more experienced users make most use of the Questions page, while newer or casual users use the Home page.
So in conclusion I would love to see a setting that sets the Question page as the default view. This can either be a profile setting, or to be more discoverable a togglebox on the Questions page.