Plenty of animals love human contact and enjoy interacting with people. If the animal in question can handle it and it's safe for the zoo visitors, people should be able to interact with the animals as much as possible. The animals would have a better life and people would be able to learn much more about the animals as well!
Yes, visitors to zoos should be allowed to interact with the animals. It is important for humans to come into close contact with all types of animals so the humans can appreciate the value of each animal.
However, interaction between humans and animals should be strictly restricted and supervised.
It's not safe for zoo visitors to be in close proximity to most wild animals. For instance, visitors should not be allowed inside a lion cage or the enclosure for a rhino. However, some close, highly supervised interaction with animals such as penguins or koala bears might be beneficial to both the animals and the visitors.
If animals must be kept in a zoo, their environment should be as natural as possible. They should interact with other animals, not with people. It would be stressful to have people constantly coming around and trying to play with you, when that is not part of your typical lifestyle.
The vast majority of animals at the zoo are in no shape to be picked up or petted. Firstly, many are endangered and contact with people would simply cause more unnecessary risks. Animals can also spread disease to people and vice-versa, while also posing a physical risk. These aren't horses and puppies guys, zoo's by their very nature carry dangerous wildlife.
If viral videos of animals mauling tourists from adults to children haven't gotten the point across, let's just repeat what zoos at least have been telling people for decades: don't harass the animals, for everyone's safety. Contact with ordinary visitors increases the animals' stress levels and chances of injury and infection. Unless this is a zoo full of domestic cats and dogs, the animals are unlikely to benefit from contact with humans. Most visitors are not qualified to handle wild or exotic animals safely, and waivers probably wouldn't stop them in case of injury if they really wanted to sue.