A funny story to ease your soul, forgive the length:

The major primary (junior?) school I went to was within walking distance. It was on the main through-road / bus-route that bisected the surrounding housing estates.
This is England mind- not many huge roads so it was a simple two-lane. There was a bus-stop opposite the school entrance, & directly at it. There were HUGE NEON YELLOW NO PARKING zig-zags for a good 100 yards on both sides of the street around the entrance (as in England, it's fairly common practice to bump your car up the kerb a bit to park, especially on thinner busier roads)

This was done precisely to try preventing injury & accidents around the entry / busy-stop area i.e. the crowding & derp you mention. Well try telling that to the vast majority of parents who thought it was there god given fucking right to go as far as even blocking the bus-stops. Despite repeated complaints from my not-idiot parents to the school, they went -shrug- what can we do? Stop bothering us.

Funny thing is a close relative of mine, let's call him for intents & purposes "dad", happened to have recently retired from a pretty high-ranking police position. So he knew a few people in a few departments. And thus the fun began.

A Traffic Police car down each of the two side-streets bracketing the school, and traffic wardens (think meter-maids with teeth) patrolling along the main stretch, very specifically began to appear around drop-off & let-out times >:)
And it still took a month of tickets (several repeat-offenders too I'm told) before the mombie/daddict brigade fiiiinally got the message.

That was 23, 24 years ago now. The school's still there, and the road's still clear. I haven't been in the UK for 5 years myself, but I'm told the traffic wardens do swing by every few mornings / afternoons on their route :)