It is a real dilemma for many schools.
Where I work, no parents come onto the playgrounds. Children are dropped off at, or walk to, the school gates.
The school gate is manned, and the playgrounds actively supervised, from 15 minutes before school starts.
However, as parents were dropping children in the street outside the school and driving off earlier than this, we took the decision to open the gates 15 minutes earlier, as the children are safer inside the school grounds than crowded around the gates on a street busy with further cars dropping off.
We state clearly that we have no responsibility for children before the time when the playgrounds are supervised - but of course, when a child trips over, bangs heads with another child, falls off playground equipment etc etc (normal playground accidents) those of us whose classrooms overlook the playground DO rush out to help, or respond to knocks on the doors - because we do care about the children in our care, whether or not we are 'technically' responsible for them.
My DC's primary, which had a breakfast club on site, had a much simpler solution - any child on the playground (or obviously dropped off next to the school and left) alone earlier than the time playground supervision by teaching staff was due to begin was immediately taken into the breakfast club, and parents charged the daily flat fee for breakfast club accordingly. Worked really well, and the responsibility for children was absolutely clear.