It is the most-dense city save for NYC, which is ten times larger. Which is my point: people think of it as dense but in reality most of it is suburban in character. There’s no need for skyscrapers to change this. A handful of 5-story buildings on major intersections would do the job.
Look beyond arbitrary administrative divisions at what actually exists on the ground. Of course, many cities are spirals rather than circles so it can be difficult decide where to draw the line. Oakland and Silicon Valley, and even San Jose are also part of "Greater San Francisco", which is a very spread out city because of the geographical imposition of the bay.