That's already the case, though a relatively recent change, called Builder's Remedy. An incorporated city is granted the right to zone but if they do not have a state compliant housing element (an eight year plan for expected growth and housing to meet that) and if they deny building permits for that planned housing, then a builder can bypass the city's permitting process. A city effectively forfeits their right to city planning if they don't have an achievable plan for sufficient housing stock.

Berkeley has a state approved housing element. If this protested building is in the plan, then there's not a whole lot the shop owner can do about it. They probably missed their council meetings in figuring out where to put housing during the planning of their city's housing element. Or they're upset that they lost in their local politics.