The problems with domesticating whales are the same with domesticating elephants. Elephants are big, intelligent, like to roam, and breed slowly. It is incredibly difficult for humans to restrain elephants, which is why elephants are often tamed by taking orphaned baby elephants and raising them but aren't readily bred in captivity, much less selectively bred in any numbers, much less quantities that could provide food.
Whales provide an order of magnitude bigger problem. The smallest baleen whales are the same size as a bull African elephant, and most are much, much larger. It would be incredibly hard to pen in a whale or make it go where you want. This would make herding whales very difficult, or selectively breeding them for tameness. And in the open ocean it's hard to pen whales.
Elephants were also much more useful as living construction equipment than being raised for food, given the expense in caring for an elephant.
But most importantly to all this is the fact that most baleen whales migrate (except maybe bowheads). They migrate to the tropics to give birth but then swim to the poles to feed in the summer. This migration is necessary to complete their life cycle. The whales have to give birth in the tropics because the babies aren't big or fat enough to survive in the cold Arctic or sub-Arctic waters, but the whales need the high-density krill and plankton of the polar oceans to fuel their immense bodies. It's probably not possible to supplement this food artificially in whales kept year-round in the tropics because it would require migration to the poles to get the volune of food necessary to feed them.
Indeed the existence of highly dense, nutrient-packed krill in the polar summer is what is thought to have allowed whales to get so large in the first place. Additionally, this migratory habit is likely what wiped out the megalodon, because megalodon couldn't keep up with the extreme long-distance migrations, couldn't easily handle large whales, and possibly couldn't go into the chilly sub-Arctic waters. This suggests that your merfolk trying to tame large whales like this would be very difficult to achieve.