If it’s feasible and profitable to build new homes, then developers will do so.
Everyone loves the simple solution of “build more houses”. Very few actually consider the execution of the master plan. What would it take for you to start building homes? It’s an enormous risk, requires tons of upfront capital, specialized labor and supplies.
When everyone wants to live in the same areas, housing prices go up. Lifting zoning restrictions isn’t some magic bullet that will alleviate that fact.