We have the same issues in Canada with our public health system. No one wants to talk about this, but my unpopular opinion is the real problem is our retirement program and lack of fertility - we're way too generous, and without a tax base there's only so much we can do.
Unless a politician actually makes the unpopular move to cut retirement benefits or massively increase fertility this is only going to get worse.
Solving the unaffordability of housing crisis is the step needed to unblock fertility.
The solution exist, yet it cannot be pushed forward in a democratic system as it creates a generational conflict.
Although I agree solving the housing problem will help fertility (personally I'm waiting to have kids until I get more permanent housing) it's definitely not the only thing stopping people from having kids. Rich people famously have low fertility and they don't have any trouble getting housing.
Fertility, like homelessness, is a multivariable function that requires a multitude of policies and approaches. It's not a simple dial that one can move back and fourth.
Unless a politician actually makes the unpopular move to cut retirement benefits or massively increase fertility this is only going to get worse.