It's not necessarily true that making housing more affordable requires lowering the value of homes.
Consider an area with relatively low density—few houses per acre. By increasing the housing supply, such as by constructing multiplexes and small apartment buildings and enhancing amenities to go with the density, the cost per housing unit can decrease. This increased density will likely increase the land value. So, while the price per unit decreases, the value of the land on which homes are situated could actually increase!
It's all about building the right kind of housing, and personally my favorite mechanisms to so so would be a land value tax as idealized in Georgism, though that definitely would lower home values.
So, while the price per unit decreases, the value of the land on which homes are situated could actually increase!
...for that particular local area. For the country as a whole it's still +supply -> -price because not as many people are forced to pay for expensive housing elsewhere.
The vast majority of Americans live in areas that in my opinion would be improved with density.
I don't disagree, but this reduces prices overall. More affordable housing is the opposite of more expensive housing, the headline is correct and there is no way around it.
It's really not that simple, if you own a single family home in an area that is increasing density, that lot does not necessarily decrease in value. And it's still more nuanced in less dense areas, which is not the majority of housing.
It's also not a zero sum game, there are millions of people who would like to move out of their parents but can't afford to, population is increasing, and who know how many other factors.
Flatly saying that home values have to go down isn't necessarily true, it depends on the exact mechanism used to increase affordability.
Fun little side thought, there was a study that came out a while ago in Maine that stated that the average resident spent around $10k personally on cars, and another $10k in government spending.
Designing an area without requiring cars by increasing density, means that for everyone who can ditch a car on average they'd save $800 a month, some of which could be spent on housing.
Increasing affordability doesn't even necessitate lower prices per units if your population has more money to spend.
This is a lot more nuance than the average person is likely to accept, so it is easier for a politician to just dodge the question and avoid pissing off either side.
The car thing makes logical sense at least, the idea that another expense would be removed as a result of dense housing, but that extra money would be spread across everything those people might want to pay for and not have much effect on housing demand. The rest of the things mentioned seem like variables that are independent of housing supply, and wouldn't affect whether increasing housing supply suppresses price (it does) (that's the whole reason to do it in the first place) (supply and demand is real).