Mr. Biden has reason to worry. But including Mr. Cuomo on the ticket—a leader who is being battle-vetted as strong, calm, competent and blessedly nonideological in the thick of the crisis—is the best bet to draw enough votes from the disconsolate ambivalents to give Democrats the winning edge.

Sometimes in chess, you have to sacrifice your queen in the interest of toppling the opponent’s king—or exchanging her in the heat of battle for a couple of bishops and a rook. Before the pandemic, Mr. Biden promised he would put a woman on the ticket. It was one of those mistakes of the moment that politicians make—like Teddy Roosevelt promising right after the 1904 election not to run for another term, or John McCain naming Sarah Palin as his running mate.

Mr. Biden would pay a price for going back on his promise. He could mitigate the perceived betrayal by making clear that Democratic women would gain at least two bishops and two rooks—that a Biden administration would establish a female team of rivals, favoring Elizabeth Warren, Amy Klobuchar, Kamala Harris and other women for cabinet posts and top White House jobs.