It's in the name: stadtpark, city park.
In defense of Berlin's Tiergarten, it was originally a hunting preserve for deer (and Hasenheide was for rabbits), so it's big and intimidating. But there are still facilities in it that serve the neighboring residents. And throughout Berlin there are multiple volksparks, people's parks, which have everything the author mentions.
In most cities, parks evolve to serve the residents.
Berlin parks are difficult to beat! I lived half a decade at 2min from Treptower Park, my morning walk to the office, through the Soviet memorial, was so awesome. I’m now in Hamburg and while we have some nice parks I do miss the ones from Berlin