Is public transit always more convenient than the individual car ? No, but you can make the conscious choice of not owning a car, even if you need to raise a family. Switzerland has a high rate of car ownership, because we have a lot of money to spend. But many people, even if they own a car, will sometimes use public transit, because it is convenient, safe and comfortable.
There are places in Switzerland where if you need to take a taxi or an Uber, you will have to wait more than 30 minutes before one gets there. At this point, it is more convenient to take the regional bus that goes every 30 minutes. Even if the public transit frequency is every hour, I can plan my journey to arrive on the correct time (also, public transit is synchronised in the whole country to avoid waiting times).
I can see autonomous rideshares displacing taxi service and such. I think automonous rideshares still need density to be profitable. So if you need to subsidise rideshare to cover the whole country, why not properly invest in public transit?