YANBU at all. We've just had a letter (which I absolutely support) asking parents not to bring their dogs to pick up/drop off for safety reasons in case a child is bitten. That's really sensible.
Why can't we apply the same common sense to cars? To be fair, our school is in a particularly difficult location (dead end street, no pavements, very narrow, nearly all walking children have to come out of school and cross the road - through the non-stop stream of traffic out of the school gates. Put bluntly, it is an accident waiting to happen, especially given the number of KS1 children on scooters.
I don't object to people bringing their children to school by car if they have to, but why not either
(a) ask them to park in the convenient public carpark 1 minute's walk up the road (not down the dead-end bit), issuing parking permits for the school carpark to staff and anyone with a particular need (not just SN, but eg. parent helpers who bring materials into school)
or (b) close the carpark exit until all walkers are out of the school gate and away (ie, make the drivers wait for 5 mins so that children can leave safely on foot).
(I am thinking of saying this to the governors, btw, but suspect I"ll be viewed as a nutter - unlike whoever asked about the dogs. Not sure if I am brave enough to, esp as my dd is now old enough to be reasonably car-aware.)