Across the US, the majority (2/3-ish) of children already live in families where both parents are employed. I don't see free childcare moving that statistic more than a few percentage points at best. I'm skeptical that this policy would encourage more parents to work and further raise housing costs, especially since this would mostly affect families with children who are pre-K. It is a big policy change but the number of families it will affect is quite small I think. If it does have any effect on housing cost I would expect to see it at the very low-end since it would help low-earners the most.

In Quebec it was a 20% jump in mother employment: https://www.bloomberg.com/news/articles/2018-12-31/affordabl...

And had all sorts of negative outcomes for the kids: https://www.edweek.org/teaching-learning/long-term-study-of-...