I think one has to draw a distincton here between enjoyment and willingness or biddability. It is my belief that a llama, like any other animal, is happiest doing what comes naturally. In their natural state, llamas are grazing in their herds alongside their buddies. When they are not doing this, they are cud-chewing, resting or engaged in sexual activity. In short, they live to eat, sleep and make other llamas.
For many thousands of years, llamas have willingly left their home territory and their grazing to carry packs and panniers for their owners for hours each day..but let us not confuse this with pleasure.
The trekking of llamas has become very popular in UK as a recreational activity. Many llamas have been successfully trained to carry panniers for the customers and seem to do this extremely willingly. I have enjoyed many such treks myself, but am under no allusion that the animal does this out of choice. The frequent comment that "llamas are curious and enjoy new adventures" just doesnt make sense to me. Llamas, in my opinion, are "curious" because they are animals of prey who, in new situations, have to constantly check that there are no predators around them. They have constantly to be on guard. In evolutionary terms, their survival has depended on this alertness.
I am thankful that many llamas are sufficiently trustful of man that they are willing to allow us to trek them and give us pleasure. But let's not suppose the llama does it out of choice.