So long as that is the requirement it won't be done, nobody will do it. You need to find a different starting place.
Start by not requiring buildings be far apart and have parking. Right not the neighborhood you envision isn't legal to build if you want to. Make it legal.
Make tax codes encourage building high. Charge higher taxes for the ground floor.
Allow everyone to build by right (meaning no public hearings, permits must be approved by buerocrats) up to the road/sidewalk or property line.
Even if the building is setback from the property line require the outside walls be built to up the lot line on all sides standards. That means fireproof if the building next door burns. That means can be demolished without anything falling to the outside, or even a need to do anything outside to demolish it.
For bonus points define places where a door to the next building must be located. (you might never visit your neighbors that way but the door still exists and can be repurposed to a public walkway when you leave and the new owner has other ideas.
The car accident death rate may be low enough that it’s really not worth mitigating against.
But also, I don’t mean Manhattan specifically. When I say “city” maybe you are thinking high rises. A neighborhood with predominately 2-4 story buildings can be incredibly walkable. You just have to stop designing everything to accommodate cars ahead of all else.