Most of the time is taken in getting approvals and permits, things that cities have direct control over and can + should optimize. Just doing that will decrease costs since a quicker turnaround means faster ROI and less risk for a developer.

You're right that cities do not expand uniformly, and city improvements are also not uniformly distributed. This is why a flat property tax does not make sense. Use land-value-tax to balance. If one area is very desirable, increase land taxes in that area and use the revenue to fund improvements like parks, libraries, schools all around the city.