Birth rate is collapsing even in countries that have plenty of housing and don’t have skyrocketing rents.
High correlation with the pill (birth control) and increased participation in the workforce by women. Also cross reference with wealth inequality levels.
The smart phones is correlation, not causation
Except the poorest people traditionally had the highest birth rates.
But traditionally housing was also pretty cheap and only select few properties in the right areas gained any significant value over time. Now rentseekers are and have bought up significant amounts of housing and drove both housing and land values up far faster than the low end of wages.
People were poor for different reasons but they were still poor. There's no reason to think that expensive housing and cheap food makes low birthrates but cheap housing and expensive food makes high birthrates.