To the best of my ability to determine the only president to have sent his children to a public high school was Gerald Ford. It was a pretty nice high school in Alexandria, Virginia but it was a public high school.
I honestly don’t know how politicians get away with preaching equality on the one hand while practicing elitism on the other. In a less docile and gullible society politicians who preach the virtues of the public schools while sending their own kids to private ones would, at the very least, be booed off the stage. Or, preferably, tarred and feathered and run out of town on a rail.
Once upon a time we had two great social levelers: public education and universal male military service. Now too frequently both are thought of as welfare, just for the poor.
I stand corrected (in comments). George W. Bush’s daughters also attended public high school. I appreciate the correction. That actually makes my point even better.