Earlier quoted context omitted.
When you automate production, prices go down. That's something that can be verified empirically, and hardly anybody will disagree. But when you automate the entire economy, prices should go down towards zero nearly everywhere¹ - that's because when capital freely creates capital, all restrictions on production and competition become meaningless. When you automate the entire economy, salaries also go down toward zero.…
Do you mean that production costs (prices) go down with automation or that the selling price to consumers goes down? If you meant the latter this is wrong. The selling price depends on the pricing power that the producer has. Consider for example monopolistic pricing power, cartel pricing power, and regulatory capture.
Even if this happens for most other needs / products, housing isn't a commodity, and I expect won't ever be. It will generally be demand driven in terms of relative housing costs, and if you're of the mindset that inequality in and of itself is the problem, the lowest tier housing will never be enough, no matter how sufficient.
Which will just lead to a larger part of newly disposable income being spent on housing.
We already know people pay based on what they can afford.