But the Democratic Party, led by Mr. Moon, holds only 119 seats in the 300-member legislature, the National Assembly. The Democrats would find it hard to get support from rival parties in passing chaebol reform bills through a fractured legislature, where a pro-business lobby also remains strong. Passing a bill will take many months of wrangling.

Mr. Moon has also promised to make prosecutors more independent and to make it more difficult for a president to abuse the power of the office, limiting the ability of chaebol to collude with the authorities and escape justice. But such reforms would likely require a revision of the Constitution, which would be very difficult to pull off given the nation’s fractious politics.

Mounting distrust of the chaebol culminated earlier this year in the arrest and indictment of Lee Jae-yong, Samsung’s de facto chief, on bribery and other charges related to a scandal that ousted South Korea’s president and led to Tuesday’s election. Mr. Lee, who also goes by the name Jay Y. Lee, is a member of the third generation of a family that controls a business empire that makes its famous mobile phones, builds the world’s tallest skyscrapers — an affiliate constructed the Burj Khalifa in Dubai — operates hospitals, hotels and theme parks, and even offers credit cards.

But frustration with the chaebol has been building for years. Critics blame the conglomerates for a number of social ills, including corruption, inequality and the crowding out of smaller and potentially more innovative businesses. Shares in the chaebol trade at lower prices than they otherwise would — the so-called Korea discount — because outside investors fear founding families will shortchange them.

Family shenanigans have not helped perceptions.

There was Cho Hyun-ah, daughter of the chairman of Korean Air’s chaebol, who resigned from an executive position at the carrier in 2014 over the infamous “nut rage” incident, in which she forced a plane to return to the gate when she was unhappy with the way a flight attendant served her macadamia nuts. There was Chey Chul-won, a member of the family that runs SK Group, who was convicted of beating a protester with a baseball bat. Then there was Chung Il-seon, a Hyundai heir who runs the group’s steel-making affiliate, who was fined by a court for abusing a string of chauffeurs.

Over the long term, many chaebol families have seen their grip on their empires slip. Often, the families have only themselves to blame. A succession fight between siblings broke up Hyundai in the early 2000s. Lotte, another chaebol, went through an ugly war between brothers in 2015. (The winner, Shin Dong-bin, may have seized a poisoned chalice: He has also been indicted on charges of bribing South Korea’s recently deposed president, Park Geun-hye.)

They face other challenges — in particular, taxes. Perhaps surprisingly in a country where dynasties have persisted, inheritance taxes in South Korea are high — for the wealthy, 50 percent or more.