In the U.S. you can definitely use school facilities after hours (such as the fields, and even some buildings, etc).
The primary concern with not allowing access at any time of day to the general public is of course, the children.
> you can definitely use school facilities after hours
Aside from a few things like some playgrounds shared with public parks next door this has often been pretty untrue. I've definitely had police escort me off school basketball courts when school isn't in session, the natatoriums haven't had much public access, it's not like the school libraries are open after hours, etc.
I'm sure some places are more open and some are less open, I wouldn't say you can "definitely" use them.
I'm not aware of any public schools in my area that would allow me to, e.g., use the basketball court or soccer field after school hours or on the weekends.