I agree that much depends on the type of training and who gets to witness what. Animal care has been greatly improved with training as animals can now receive more frequent routine health inspections without disruption or sedation. Showing this to visitors gives them insight into how a zoo cares for the animals.
Some zoos give performances by animals that highlight their specific survival skills, physiology, etc. and these, while entertaining, are educational and therefore part of the zoo's mission.
On the other hand, there have been several tragic zookeeper attacks due to unauthorized or poorly monitored training by those zookeepers. Keepers can get very attached to some animals and lose perspective. Management must be attentive to that, have strict protocols in place, and also monitor keeper attitudes towards the animals in their care. People get too comfy, too delusionally self-confident, and too cocky and then bad things happen.