Just take the car in these situations, that's not the problem. The problem is people justifying 90% of the car usages (which could be replaced by bicycle or public transportation) by being snarky about the remaining 10% (and I'm being generous with 10%).
People have emergencies, and everyday people have dire emergencies like that. Trains do not fit those cases, which happen ALOT, every second.
You want to change everything without having a solution to fill the void.
It really is a waste to have people commuting like that, it's a city problem though, not a car problem.
Yes, cars should be limited in your cities, and yes you need better public transportation, but that doesn't mean getting rid of cars everywhere.
You need to structure around roads because you need to connect goods and services to the last mile, but you also don't need to have every citizen in your congested city driving to work. I don't see why you're conflating those two.
Having a baby? Hop on a train, hopefully it's not delayed.
Mother dying? Walk a few blocks, train, hopefully she'll make it.
Public transportation in American cities barely works as is, and usually only for tourists (see LA) and yet you want to rely solely on it?