When you say you disagree, is it with (1), (2) or both? If you meant you disagree with (1) but agree with (2), which seems to be the case based on your comment, why is there an inverse correlation between population density and TFR in developed countries?[0] It seems obvious that housing prices in a given city will in general increase and house size will decrease according to population density. If that is the case, it follows that potential parents will need to work longer before having children, which in turn decreases TFR. Look at apartment size in the US vs East Asia, for example.[1-3] It seems impossible for population density to increase while dwelling size remains constant, unless there is gap between the "legal" boundaries of a city in terms of what is counted toward population density and the "real" city which then would have to start out as smaller and grow larger at the outskirts.

[0] https://doi.org/10.1098/rstb.2002.1117 - "When explaining the level of fertility, population density comes out second in importance after female literacy, yet still well ahead of the traditionally studied factors: female labour force participation, income, urbanization and food security. This strong negative effect of population density on the level of fertility five years later is statistically significant in almost all years, both at the global level and among the sub-group of developing countries. " Note that this is after trying to account for other factors: "It is worthwhile to have a closer look at this apparently strong bivariate relationship between density and fertility because it might not really reflect a causal relationship, but rather could be due to some other developmental variables in the background, such as level of income or level of education that might simultaneously lead to lower fertility and make higher population densities possible. For this reason tables 3, 4 and 5 give sets of multiple regressions that study the relationship of population growth and fertility to population density while controlling some of the other social and economic variables measured." (Developing countries also show an inverse correlation, as mentioned in the quote)

[1] https://www.cbsnews.com/minnesota/news/average-u-s-apartment... - "According to a new report, the average size of a new apartment in 2022 was less than 900 square feet."

[2] https://www.statista.com/statistics/1350102/usa-apartment-si... - The smallest city by apartment size is Seattle at 689 square feet and then Minneapolis at 720. Both do not have a very high densities compared to the largest US cities by density. Queens, Brooklyn, Manhattan, SF and DC are next in that list, however, and they are all high density. I will also note that apartments do not automatically shrink when population density increases and there are a lot of historical factors that perhaps play a larger role for the size of apartments as well as the difference between the legal boundaries of a city and the boundaries of the city as relevant to this discussion. This said, landlords theoretically should opt to convert one large apartment to two smaller ones (or two large ones to three smaller ones) although I don't know how common that actually is given you need to install new plumbing, gain permits etc. to do that.

[3] https://asia.nikkei.com/Business/Markets/Property/Living-lar... - "The average median per capita size of a Hong Kong dwelling is 172 sq. feet, smaller than Tokyo at 210 sq. feet, Singapore's 270 sq. feet and Shenzhen at 300 sq. feet."