" People with small babies, anyone with urgent medical needs, and the handicapped."- yes, usually all of them will have a more comfortable life in a city that gives priority to pedestrian and bike infra. We are all pedestrians, but not all of us have cars. Disabled ppl in us are living worse than disabled ppl in nl again due to car oriented infra. Having a baby doesn't necessarily means you need to have a car, in a dense area like in NL ppl get by with a backfiets or cargo bike or just are using public transport or taking a taxi/day rental when really needed.

Related to car speed- at some point you have intersections of pedestrian and car infra and if the priority is to have a safer area, cars must drive slower, that's why lots of cities are implementing 30km areas+traffic calming like curbs, bollards and bumps and it works and heavily reduces the accidenta while avg speed remains paradoxically almost unchanged because less accidens/dangerous driving means less road blocks. Also, not all areas are wide enough to have everything separated, that's why the shared road concept exists- cars drive super slow and pedestrians and bikes have priority there, ppl can walk in the middle just like cars and cars will need to wait