I'd say city planners. They can look at the area as a whole as opposed to the one individual building. You get areas like Atlanta where developers put up hundreds of units in areas with only a single, two lane road to access it and it takes you half an hour to get a mile from your apartment where you can turn onto a larger street. Completely full developments, by the way.
What does two lane road access have anything to do with parking? Developers don't build roads (they may be required to make improvements) but they do build parking. Why do you think they don't adequately consider parking demand in their development plans?
If the city planners want to restrict density due to inadequate transportation infrastructure, that may make sense. In that case, you can simply have a restriction on the number of housing units and occupants that can be built in each city block and eliminate all the other restrictions I mention in my OP. However, by doing so, you effectively make such areas off limits to poor people by increasing costs as a result of the reduced supply.
Why should a poor person who doesn't own a car but takes the bus or maybe carpools with a friend be forced to pay for parking which gets passed along to them in the form of higher rents (since it increases development cost per unit)?
Parking demand is only one factor in car usage. If a developer wants to build in an area, then access to the area is as important as if they have somewhere to park when they get there. That's why city planners, who are focused on the area as a whole, are a better option for deciding these things than developers, who are only focused on their one little slice.