Housing may be a little harder to accomplish usefully for the people that would live there for this idea, but business would likely work well. The problem with housing (if it encompasses a large area and not just small subsets of the available area) is that some people functionally need a car for their job or life. Cutting off large amounts of housing from those that commute or those that need to make semi-regular long trips for other reasons (maybe picking up children weekly for a custody agreement, or taking care of a relative that is semi-dependent).

Maybe paid dedicated parking separate from the housing and only allowed to people that live in the area (with an increase in price for a second car for a household) would suffice, as long as it was planned well. But that's the problem, poor planning (or changes over time) could cause problems again.

Car shares are definitely not for driving to work but I fail to see why you can't use them to pick up your kids. Car sharing solves the problem where people can easily journey to work without a car, but they want one for other purposes like shopping.

Wouldn’t most residents of the building need the shared car at roughly the same time to pick up their kids from school?

If most people need it at roughly the same time to get to a small number of places, then it's an obvious use for public transport.

No because fewer than 20% of households in Los Angeles have school-age children. That puts a ceiling on your worst case right there.

Provided that the housing wasn’t in some way differentially appealing to families with children (cheap 3BR, good schools, parks nearby, other amenities)

Does Uber carry approved child safety seats?

No, but to make sure we are talking about the same thing, a car share is a bit like renting a car by the hour. Uber is a computer-dispatched taxi service. Uber is not "car sharing". It is also not their other bullshit moniker "ride sharing"

I think there’s a fair argument that Uber Pool is pretty close to, or at least has substantial elements of, what one would naturally call ride sharing.

Hmm...source?