I grew up and lived very long in Berlin. I rarely needed a car, never owned one there and I know many people who moved to Berlin and then got rid of their cars, as they didn't use it anymore. Berlin is not an example of a 15-minute-city but much better in a way of everything is close by, instead of having one center, it has several.
You can apply same for Zurich. Zurich is small in comparison to other european capitals (or capitals around the world in general). So in around 30 minutes walking you can be everywhere. Still a lot of cars there, but it is just so much more convenient, that you don't need it. But if you wanna use it, sure go ahead. And according to many rankings it is one of the best cities to live in (and I would agree with that).
"The plan will require local residents to apply for permits to drive on certain streets" and the glossed over "filters"
This immediately creates an economic structure where only the wealthy would be able to freely drive while ushering everyone else into something of a forced utopia.
There are plenty of organic "15-minute neighborhoods" all over Europe (and even in the USA) where people voluntarily surrender cars (I'm one of those people) but forcing people to do this only fuels weird culture wars. Build truly car free infrastructure first and residents will ditch cars freely.