This is kind of complex. Maybe the simpler answer is that people decide to buy houses when they have families in the US, and as people have families later in life, their income has actually increased, even if wages appear to be stagnant. Wages are measuring the wrong thing.

its not clear at all if 'house prices' are meant to mean construction, land, the two combined, new, or new and second-hand

or at least the conclusion breaks all assumptions...are they saying the cost of new building trumps both land price and depreciation?