‘Should you exist?’ Billionaires face rising criticism alongside rising power.

The United States was at the precipice of a financial crisis – and the wealthy and well-connected worked out a plan to avert disaster.

That was the narrative in 1907, as Joseph Pierpont Morgan brought fellow financiers into a room and coaxed them to prop up a tottering banking system. Their action eased a potentially devastating financial panic. But it also troubled many Americans by revealing how, even within an already mighty nation, a relative few wielded extraordinary power.

Today, those concerns still resonate. They punctuated the 2016 presidential...