“There’s just absolutely no downside and only upside,” Antonia Ferrier, a longtime Republican strategist and former senior aide to Senator Mitch McConnell, said of quixotic presidential runs. “It is an industry of self-promotion. What better way to self-promote than run for president?”

Mike Huckabee, the former Arkansas governor, has leveraged two losing presidential campaigns into an empire of folksy conservative ubiquity across television, radio and print. Ben Carson transitioned from renowned neurosurgeon to national hero of the right during a 2016 run that included an extended midcampaign hiatus to promote his book. His efforts were rewarded with a job in President Trump’s cabinet.

Newt Gingrich, the former Republican House speaker, clawed back to national prominence seven years ago despite posing little threat to take the nomination, turning the protagonist of his wife’s children’s book — a fictional elephant named Ellis — into a kind of campaign mascot available for voter consumption.

“It gives you a certain stature the rest of your life, kind of like having once been speaker of the House,” Mr. Gingrich said in an interview. “They introduce you, and then they say, ‘… and former presidential candidate!’ It’s not bad.”