Maybe cities should try to build public transport that mothers with children prefer to their private cars?

If cities cannot offer something better, they will never convince. So they must restrict. Then at least they should forbid the better for everyone not just for people their voters do not care about. It is quite revealing that the myriad of small, cheap, and flexible transporters that provide all these services inside cities are nearly always exempt from traffic policies.

Mothers with children already have an alternative: Use public transport, or use an uber, or a taxi. There's no reason to own a car.

It's all about utilization: An uber cab will probably see 10%-90% utilization (passenger count / time in transport), while a privately owned car is utilized only a few minutes of the day, by only 1/5th of the passanger capacity. Most of the time it collects rust on a parking spot that could be utilized for a better purpose. Parks, street food stands, benches.

Same for delivery: If the alternative is that everyone oes out and pollutes supermarkets, streets and public transport to get their freshly ground coffee, don't you think that having a vehicle that delivers on the last mile to the customer is much more efficient?

In cities that invest into bike lanes, obviously cargo bikes are becoming a real alternative for delivery services.

Yes, public transport has to be improved, too, nobody argued otherwise.

Now why is utilization suddenly a concern for cars but not for cargo bikes or exotic consumer goods like coffee? Let me guess, you don't own a car, but a bike and you like to drink coffee? How about your bed, could that not be utilized much more efficiently? I bet 16 hours or so it just stands there collecting dust.

In a city, everything that needs space is scarce. You can ask for a "fair" price for a parking space, but then don't complain about a "fair" rent and a "fair" premium on every service that also utilizes space. The thing is that "fair" can look very different to different people.