The quick answer is No. Modular homes are NOT the answer to Bay Area's affordable housing demand. It's the land that's expensive, not the house on the land. If you want to pay less, you need to go where the land is less expensive. Land is cheap in Alaska. Land is cheap in Nevada. Land is super expensive in the SF Bay Area, and they aren't making more of it.

This article left me wanting to see modular units that stack. (making more use of our scarce and expensive local land.) Local examples were not hard to find, and looked great!
Web Link

Ah - maybe the answer to CALIFORNIA residential housing is MAYBE. (U can go freezed Your behind off in Alaska or North Dakota!)

Small size lots / less side clearance/ two stories. See the link/ modern construction (not premanent-modules) in the Castro City area of Mountain View. Single family zonning.

Web Link
Sorry! That's how the Google Street View link came out!
(this is 131 College Ave, area of Mountain View)

Modularized permanent construction of School Classroom Buildings also saves substantial building money (1/5) and even more if 'pre-approved' in the design process (use some standard designs - not custom).

My very meger city planning background DOES NOT LIKE the 'cookie' cutter' (Levittown) appearance, but add a colorful paint job, on top of some 'different pop-in window' varients, and some screw-on millwork = 21st centuary Victorian Eastlake. (that era's 'fancier' designs depended on factory mass-produced and rail-shipped 'catalog' wood work) [ref. Chase, The Sidewalk Companion to Santa Cruz Architecture, (c) 1979, Paper Vision Press, Santa Cruz]

As echoed in other messages, single story modular units make no sense when the chief cost is land. Multi story multi units on the same square footage land will do much better. As long as costly regulations and requirements can be suppressed.