I live and travel around Europe. Seeing parents riding with their very young kids is not too common a sight and every major city I've been to has traffic problems, because a whole lot of people do want to use cars and do value their convenience.
Whether that's a bad thing or not is another discussion but don't try to present Europeans as some sort of superhumans.
I only have experience with Berlin, Hamburg, Munich, and Amsterdam; but if you sit outside of a daycare in those cities in the morning you can see the multitude of people who ride their bikes to drop off their 1, 2, and sometimes 3 kids at daycare. Those cities do cycling right and it shows.
So I would disagree with you. The traffic problems are caused by having cities that are only setup to make cars convenient and everything else inconvenient. Cities that prioritize the lowest bandwidth people mover are going to have major traffic problems, of course.
Like you say, people want convenience. But I don't know why you think they particularly care about driving (or cycling or walking or taking the train). They just want the most convenient & cost effective thing. If that's a car, they will drive a car. If that's cycling, they will cycle. If it's the train, they will take that instead.
On practically every measure, owning a car is far less convenient (unless you live in a city built around driving cars) and more expensive than not owning a car. We owned a car in Germany but only used it for weekend trips. So the point here is to change cities to not be built around cars. Make cars less convenient.
Your last line is the issue that annoys people. It often lands like “rather than focusing on making other means more convenient, we’re going to focus on destroying the existing convenience to make alternatives more competitive.”
A certain amount of that, as an unavoidable byproduct, is okay with most people. What’s not ok is the perceived (or real) gratuitous destruction of convenience.
You can't have it both ways. You can't have a car-friendly city that is also great for cycling and public transit.
Besides, gratuitous destruction of that "convenience" is good for society and the planet. The obesity rate in America should be proof enough that cars are bad for you.
While we love our bycicles in Europe, if you go down to the southern countries you won't see much of them taking kids around either with trailers or kid seats.
Most of the Germany had the "benefit" of being able to rebuilt post WW2 bombing, so they are a bit more spread out and can easily accommodate new road features (if there was a country that is car friendly but not US, it's Germany :)).
And Netherlands is just... Flat, and biking has been a tradition there long before the current ecological push.
However, most European old towns are frequently narrow one-way streets on hills and it gets really hard to get a buy in to reconfigure them altogether.
But I agree with the premise that streets should be given back to people, but pedestrians should first and foremost, with bikes and other micromobility tools "demoted" compared to them as to not cause mayhem (eg. pedestrians do abruptly stop :). Basically, pedestrian streets with traffic rules stating that pedestrians are always in right of way. That should provide plenty of space for both social activity and transit with bikes and such, even in small streets I mention.
Living in a climate that gets significant snow and is hilly means I would also like to streets to be efficiently "heated" to reduce risks for pedestrians and cyclists during winter months.
Whether that's a bad thing or not is another discussion but don't try to present Europeans as some sort of superhumans.