With Kraft Heinz Co. reportedly considering a breakup of its business, some analysts believe more of its food-industry peers should do the same.

Kraft Heinz is preparing to break itself up, a decade after an infamous merger of two of the biggest names in packaged foods that was orchestrated by Warren Buffett and Brazilian private-equity firm 3G Capital Partners.

The Heinz ketchup and Oscar Mayer hot dogs featured at barbecues this summer are owned by the same company. Next summer, that might not be the case.