Doesn't even need to be 5-10x the population density. The "inner ring" of Paris is similar density to San Francisco and supports a metro system that I think most would agree makes car trips unnecessary. But the "rebuild the city" part might still be somewhat necessary.
Living in a European city and relying 100% on public transit and walking, with occasional biking for longer distances, it’s easy. It does not require 5-10x the population density, maybe just 2-3x, at least compared to San Francisco (which is already somewhat dense in parts). It is not a major shift in lifestyle easier. The tallest buildings in some cities in the Netherlands are 2-3 stories, and those cities still have regular buses, trams, and trains.
There are even some suburbs full of single family homes, with yards, which still have buses every 8 minutes all day long, and long-distance commuter train service every 20 minutes.
Yes the US needs more density for this to be feasible. But San Francisco isn’t that far off on the density that it would needs
This is easier said than done. Making the density 2-3x is still a huge undertaking. With suburbs with single-family homes, this means bulldozing half of it and somehow redrawing all the property lines so the lots are 1/2 - 1/3 as large and building new houses within the new lots. You can't just magically take a subdivision full of McMansions and somehow increase density 2-3x, unless all those houses take in boarders.
Also, SF is still pretty unique compared to most American cities. So you might be able to do this stuff in SF, but not so much in places like Houston.
It's not just a matter of "fix service", it's you need to completely rebuild the city with 5-10x the population density.