Double-buggies on public transport and more than two kids on a typical cargo cycle aren't fun either. Granted the age-span that's necessary is a little shorter than car seats.

That said, have 3 kids aged within 5 years of one another and we never had to get a double buggy. The older ones would be OK to walk (3 year olds will walk a pretty long way if you're patient) by the time the youngest got too big to be sling-carried.

It comes down to, dealing with three under-5's single-handed while out and about is pretty hectic full stop. Most places with high birth rates "solve" this by not allowing mums the expectation to be away from the house much, and/or they're multigenerational households where grandma or an aunt can be home with some of the kids.

So to your point, I think it's less the requirement to own a car, more the expectation of a kind of lifestyle which often, though not always, in turn requires one. Childcare for 2 year olds here is often upwards of $2500/month, now that's a contraceptive.