There is already an incentive to build densely and provide more housing, developers already want to do this because they make more money by doing so. They are literally not allowed to build anything other than single family homes though, the local homeowners actually control what is allowed to be built.
That is to say: the people who have an incentive to keep housing supply low are the ones deciding what is allowed to be constructed in their town.
If I go buy a piece of land in Cupertino and I want to build an apartment complex, I have to go apply for permits and get approval from the city of Cupertino zoning board. The people on that board are all people who live in Cupertino that own single family homes, they have a strong incentive to deny my application if I am building my apartment complex anywhere near their neighborhood.
Basically every single city in California has zoning laws that prohibit you from building anything other than suburban single family homes in most of the town.
You can fix the housing crisis by passing a law that limits the power of the zoning board to deny permits for these types of housing.
Take a look at the Cupertino zoning map: https://map.gridics.com/us/ca/cupertino#11.93/37.31591/-122....
if you click layers -> planning -> zoning you can see an overlay of the zoning for the whole city. The light beige color is "single family" zoned, meaning that nobody is allowed to build anything other than low-density homes. Notice how _most_ of the city is designated "single family". This is the cause of the entire problem. Nobody is allowed to build anything more dense than the single family homes that are already there.
Not-so-coincidentally, Cupertino is one of the most expensive places to live in the US.
Look at Houston, TX. They have no zoning laws (it's not perfect they still have deed restrictions which sometimes act similarly to zoning laws), and it is a massive city. The median house price is ~340k, something that most normal people can afford. There is a clear correlation between reduced zoning restrictions and lower housing costs.