But again, no one really does that. And unless people do it en masse, that population is not really wealthier.

How much is en masse? There are enough people relocating to my town buying homes with cash, from the sale of their much more expensive homes, that it makes buying a home for the current residents very difficult.

I'd say they were more wealthy for their property value and converted that value into liquid wealth by moving locations.

Why would selling houses en masse be necessary condition to call the owners wealthy? The mere ownership makes them wealthy, not their selling activities.

We care about wealth because we care about power. An liquidity asset is like an empty threat.

It is very true while real-estate in the abstract is liquid enough, nobody likes to move so owner-occupiers are hard to compare to landlords, traders of real estate, etc.

This is just ad-hoc changing the definition of wealth to suit your particular need at this particular time.