Carbon /zinc is what flashlight batterys were before alkaline batterys became so cheap and popular. Nothing wrong with them except they have less capacity than alkaline and have only 1-2 years shelf life compared to alkaline with 10+ years shelf life.
There are a few applications where carbon /zinc batteries are still recommended. A carbon / zinc battery can be totally discharged and will not leak for atleast a few weeks. An alkaline battery totally discharged can build pressure that must be relieved at the safety blow out plug When this plug pops, it relieves the pressure, but also spills the corrosive electrolyte into the device, so carbon / zinc is often recommended for emergency power supplys..