I believe that the church/state separation that we enjoy in the US is indeed a result of the English system, namely that we did not want to have the English system.
And of course note, that privateschools are not restricted from prayers. If a private school wants prayer, the government can't interfere.
In the public sector I would suggest that ths Law takes a "safety first" approach when dealing with this. Because teachers are considered people of authority, when it comes r to kids, even if prayer in school were voluntary, because of the authority granted to teachers, prayer in school would still be an issue of legal mandate. In a private systemthe Law is powerless, but in the public sector by allowing things like prayer in school it can be viewed as an endorsement of such belief. Unless a school decided to have voluntary prayer for thousands of beliefs, with students opting in and out of what suited them. Which would be an inefficient use of time and resources.