No-car weekdays would have a much greater environmental impact. Local governments should ban all "single-person cars" Monday-Friday each week. There are sufficient transportation alternatives which, although less convenient, will be much better for the planet. People just need to get used to it.
That seems impractical. But with a small logical leap you could arrive at a scheme whereby not all of the private cars could be on the road the same day. You could use the plate number to index this. Almost like what days you can water your lawn and what days you can't.
It's done elsewhere in this world. And people did get used to it.