Manufactured housing is probably the best bet for "built cheaply yet with a randomization", but most high-cost-of-living areas lack the available land. So then you need to build up, and that opens the Pandora's box of building code compliance, labor costs and material cost.

The city of Los Angeles presumably has access to average material costs and average labor costs, but the simple apartment complex they developed to house the homeless still ended up at $746,000 a unit https://www.nbclosangeles.com/investigations/las-homeless-ho...