I grew up in the Sunset in the 50's and 60's and yes there were kids all over the place. I lived on Lincoln Way between 35th and 36 in a pair of flats (very SF name) my family owned. My grammar school class at Holy Name had 50 in it and we had two classes first through 8th. This was just one Catholic school there were many in the Sunset and Richmond. Add to it the many public schools such as Lawton.
It could just be my memory but it was a great place to grow up.