I think you are missing the point. The reason you don't see broken sites is because developers take extra time making sites work in Safari. They shouldn't have to.

>My impression is the desire to have good mobile support keeps Safari support alive.

I would very much argue the opposite. A good browser in iOS is directly against what Apple want (people in the app store, not in browsers). Safari is at best the absolute bare minimum a company like Apple can get away with and not a line of code more. Having just redesigned our business site I have just finished fixing the site to be the same in Safari as in the other browsers. I was forced to do this extra work to not exclude Apple customers but if I could have left it as is I wouldn't have wasted my time.