My running of the starter set went so much smoother because I sat and read both the PHB and DMB first. The starter set is for eliminating obstacles to a group sitting down and starting quickly, and works for those who learn by doing. It is not a good resource in that regard for people who want to learn on their own, or be confident before they start.
Some people absolutely will be served better by buying a starter set first, but for others that's just as true for the DMG, and therefore, it absolutely should contain, as part of its purpose, the resources for someone who has never run the game before.