But even in the case where the area becomes more popular, a larger supply will result in lower prices than if the area had become more popular and did not increase supply.
Not necessarily and not from an economic perspective. One can argue that, but it depends on how building affects the market. For example by shifting demographics. But even so renters, without rent control, are only interested in the part of the market they can afford where they live. That is, the quantity supplied at their income level. Which is even more susceptible to changes. The assumption people are making about "basic economics" just aren't true. More supply just isn't a solid argument for affordability without supporting evidence, and especially not when it comes to housing.