Realistically, I don't think most people think that way. ("Don't build that apartment! The resulting increase in the local supply of housing will decrease my property value.") It's more that they don't want to live next to whatever is being built or don't want the character of the neighborhood they live in to change.
Which is somewhat understandable, but there's a balance here between the rights of existing residents vs the property rights of the owner of the property being developed (and future residents thereof). There are also regulatory burdens associated with any legal processes intended to give more rights to existing residents.
I think you’re mostly right that people don’t think in those terms exactly, but “oh if they build more housing traffic will be a nightmare” or “it’s already hard enough to get into the good schools” or “I can’t even get a doctor’s appointment before you build a hundred new houses” and so on: not directly about cost, but I think they do think about all of the things that drive value (and therefore cost) in the existing housing stock.