At Canada’s official residence for its prime minister, security cameras keep silent watch over the fences, visitors pass through gates that can block truck bombs and a detail of uniformed Royal Canadian Mounted Police officers patrol day and night.

But the prime minister himself is unlikely to be found inside.

When Justin Trudeau became prime minister three years ago, he took a pass on moving his family into the official residence at 24 Sussex Drive, built in 1868 by an American-born lumber baron. Decades of neglect had turned Canada’s top political address into its most famous home renovation project.

But no recent prime ministers have been willing to commit the tens of millions of dollars it would take to make the stone house habitable again. It would look as if they were spending money on themselves, a politically toxic step in Canada.

Mr. Trudeau, 46, who lived at 24 Sussex as a child when his father was prime minister, is no exception.