Unlike the taxes on far lesser properties, the $71K should pay for the "education" of any kids living in the house and a whole lot who are not.
It is doubtful the kids from that house would be sent to public school, so more savings to the town and district.
And the cost of infrastructure, etc.
Most likely they have multiple houses. If you can afford to buy a $20 million house you probably have one in a city area. Like in the Beacon Hill area of Boston. Right down the street from John Kerry.
Then you have this house in North Hampton, NH for the weekends. Then the house in Aspen or Sun Valley for when you want to go skiing in the winter. Maybe if you do not want to spend as much you have a house at Loon, NH or Okemo, VT. Then the house in Naples or Palm Beach that you go to in the winter when you want it warm.
Then there are the boats. I mean plural too. You have at least one in Florida. Another in Rye Harbor, NH or if it is really big you have it at Wentworth By the Sea. On Newcastle, NH. That is typically where the bigger yachts are kept.
People that have seven to eight figure incomes live in an entirely different world than YOU and ME. $71K in real estate taxes might be a deal if it lowers their income tax by half. If your income is multiple millions annually.
You are correct too when it comes to funding the public schools. People who can afford to buy a house like this send their kids to Phillips Exeter, Cushing, Lawrence Acadamy, the Groton School, etc. Prep schools that cost more than many private colleges.
This is similar to some of the big lakes in NH. Lakes where people have $5 million lake houses in Moultonboro, NH. Mitt Romney had one there. It was valued around $5MM when he ran for POTUS. He paid a lot of taxes there, but did not have any kids in the local schools.