The grass part of my yard feeds many rabbits and birds (grass and worms, respectively). Other than when covered with snowpack, it’s rare to go two days without seeing a rabbit and birds are feeding every morning, especially after rains (that bring the worms higher). This is in a small city yard that’s mostly grass.

Sure, rabbits are happy enough with mowed grass, but if you asked them, they'd probably rather you didn't cut the tender tips off all the time. :) And the species of birds that hunt worms in the ground are a very small subset of what you could find in a city. (I would venture you're mostly seeing robins.)