Kitchen sink draining into catch basin
The point of that system was convenience. Plumbing was expensive and time-consuming 100 years ago. Whether it's common depends on the neighborhood and the city, of course.

Whether it's acceptable now depends on your local ordinances. Most "gray water" is required to pass through an approved septic system. I'm surprised that local code doesn't require an update for home sales. Frankly, I wouldn't want food and other waste decaying in my back yard, but that's just me.