In 30-year mortgages you are realistically paying more than half your monthly payment as interest, and doing that with pre-tax money means you're conservatively looking at 15% total reduction in monthly payments compared to renting.
You are right that the US has two things to advantage owning: (1) mortgage interest tax deduction and (2) 30-year mortgage terms.
If you're lucky enough to lock in a mortgage rate of ~3%, when you add in the mortgage interest tax deduction, you're practically paying nothing for the money you are borrowing.
However, all it takes is a 10%+ drop in the market when you are selling to wipe out any advantage to owning and often you'll come out behind of someone who rents.
Anything over $250k puts you in the top 2% of U.S. households. Your definition of words like "trivial" and "wealthy" might be different from mine.
It's a write-off for someone who's making enough money to find it worthwhile to itemize but not enough to pay AMT.
Wealthy families also have access to higher-quality asset-backed loans which typically come with lower interest rates.