Possibly the "wealthy" appear to be living hand to mouth intentionally. Inflation is a highly regressive tax on cash and savings that rewards hard/real assets.
Buying the most expensive house you can (barely) afford is a wealth building strategy. It's not without risk, but you have inflation on your side. Sitting on cash to save up for that down payment is an uphill fight against inflation.
As a parent of a 3.5 and 1 year old, I'm definitely a believer that our public schools are de facto private institutions. You pay your tuition one way or another for a premium product.