When I visited London with my parents, we went by train. When I was in the cub scouts, one of my memories was a group trip by train. When I went to middle school (years 4-6), it was easy enough for me to walk alone at the end, though mum did go with me at the start; when I went to secondary school (7-11) there was a bus, though eventually I found I liked the (3 mile!) walk.
Today, I find that my local bus route within Berlin to a nearby mall takes me past 2 schools, and at certain times of day the bus will fill with kids and adult supervisors. Sometimes I see people taking Kinderwagen on the bus.
Designing a city that helps people make those journeys car free, makes it better for the 10% of journeys that do need to be made with a car.
Unless you're going surfing, 3 kids and their sporting equipment fit in a small hatchback, with room to spare.
If the roads in cities are wide enough in cities for literal trucks, then they're wide enough for your car. Widening roads and making cars bigger makes pretty much everyone less safe.
Don't get me wrong, you're free to live in the boonies and drive 400km to your sports club, but don't call me narrow minded because I can load up 5 people in my VW passat and drive 500km for a 10 day vacation, or because I prefer not to get bulldozed by a car with a higher hood than me while walking to my local sports club.
As a practical example, in the UK, on average a young g child lives 1.7miles away from their school.
That is an easily walkable distance for most children, yet lots of parents choose to drive it because they feel the streets aren’t safe to walk on in rush hour.
If by redesigning streets to make active travel more appealing, you could reduce the number of cars on the school run by 10%; it would improve the traffic situation for the ones who still need to drive. Win-win
As a Dutch person, surely you've seen that Amsterdam decided that the city's car problem in the 70s was unfixable and decided to switch to cycling. The building and delivery problem is real, but I don't think even a 10 euro/day charge for work vehicles would register given how expensive building work is already.
Land in cities is very expensive. Why should vehicles get to use more of it for free?