100,000 per square mile is not at all miserably crowded. I was working here right after Hurricane Sandy when all the commuters were staying home, and it was not crowded at all. My neighborhood in Chicago, which is probably around 50,000 nighttime density, feels positively empty on the weekends.
You could double the density of most parts of San Francisco and still not even be approaching "uncomfortably dense" (that would take the CBD to ~100,000 and areas like the mission to ~50,000).