Really the only justification for a car is when you have kids. I have 3 of them, and a car is super super useful. But yeah, for everyone else, use public transport.
That sounds nice in theory, but if your public transportation sucks you're still going to have a car.
Where I live, most places around me that are too far to walk (over 30 mins) but that take 5 minutes by car have terrible public transport. For example, the mall closest to where I live is 45 minutes by foot, 5 minutes by car, and around 30 to 40 minutes on bus (assuming no wait time at all). The reason is that it doesn't go straight to the mall, it goes into many streets on its route and the mall is its last stop.
Similarly, it takes 10 minutes by car to get to the closest train station but about an hour to do it by bus.
That's why I don't think you can simply use a "no kids? no car" logic as a universal one. Rather, the logic would be "use your car as an alternative to public transport". Which means, try to use public transport as primary means, but use the car instead if it's not viable or the difference would be big.
I believe you but to me that just means where you live sucks.
I'm lucky enough I can choose to only live places with good transit options. Sometimes I forget not everyone has that option and when people are like "but the nearest thing is a 45 minute walk" I'm like "so fucking move!" But of course it's not that simple.
But I really would rather people considered the lack of transit options a higher priority. If you lived somewhere without running water you'd probably not put up with it.
In a better set up society, public transport is perfect for kids, it teaches them how to plan and how to use public transport, it also gives you all the time to focus on them while travelling instead of being split between the road and the kids.
Sadly not a NL wide thing, but Amsterdam has free public transport for (accompanied) kids in the summer this year, and (accompanied) kids under 12 travel for free on all trains in NL (and have a 34% discount on other modes of transport).