Authors who identify themselves (or who are identified by others) as members of particular ethnic groups sometimes use stereotypes for all the reasons already suggested. It is almost impossible, in fact, for any author of any group to avoid using stereotypical characters to one degree or another. Indeed, Aristotle thought that such characters were mainstays of literature. A baby, for example, is often thought to behave in certain stereotypical ways that differ from stereotypical behaviors found in adults. Although Aristotle did not use this particular example, he would have felt that if a dramatist presented a baby acting like an adult, the dramatist was committing a violation of "decorum."
Until fairly recently, many of the great thinkers of the world have assumed that certain traits are widely shared by certain kinds of people. (For example, they might assume that young children are likely to be loud, boisterous, energetic, impulsive, etc. and that aged people generally display traits unlike those just mentioned.) More recently, we have come to think that stereotypes are often negative, and they certainly are if people are expected or forced to conform to them. Ethnic authors have often mocked and undercut ethnic stereotypes because those stereotypes have been used to help justify, reinforce, and perpetuate discrimination. Often, in order to call attention to the injustice of stereotypes, ethnic authors have had to show what those stereotypes are in the first place.
It does seem unusual that multi-ethnic writers would use the same stereotypes that offend various races, but as mentioned in the other posts, every culture has their own stereotypes. I also agree with another post who suggests that it is easier to create a one-dimensional stereotype than it is to construct an original, well-rounded character.
For the same reasons that any other authors choose to use stereotypes - because the use helps in the telling of their story. Use of stereotypes may make it easier to give the reader important understandings about a character's motivation or personality. Use of stereotypical characters may make writing about those characters easier and allow the author to focus more thought and energy on developing other aspects of the book.
At times multi-ethnic authors, like postcolonial authors, may use stereotypes to call attention to them. Edwidge Danticat does this when writing about Haiti. In Farming of Bones, some key or pivotal characters were drawn as stereotypes in order to make their situations lamentable and render the stereotypes unthinkable or even absurd.
I agree with other editors in thinking that such authors use stereotypes not by accident but for a specific purpose. It may be to satirise such stereotypes, or to question them, making them problematic and pointing towards the limitations of the usage of such stereotypes. The important thing you need to do is to identify stereotypes and then analyse them, asking these kind of questions.
It is a little easier to explore stereotypes, artistically or otherwise, within ones own ethnic group or gender. African-American authors using the "N word", for example, is very different than someone who is not an African-American. It robs the word, and the stereotypes that accompany it, of their racist power.
I also think that some authors find it liberating to talk of those stereotypes that even people of their own ethnicity tend to find some truth in.
I may sound a little negative here, but I think authors (multi ethnic or other) use stereotypes because it's easier than drawing characters with complex motivations and personalities.
We can judge a certain segment of soceity much easier if we can paint them entirely bad or entirely good...or pigeon-hole them into a certain stereotype.
There could be a few reasons, but one that comes to mind for me is that stereotypes are universal (every culture has the mother figure, the hero, the villain, the brainy type, the coward, the gossip, etc.) and the use of the stereotype may help to further understanding of a character. It could serve, also, to refute the validity of the stereotype in a particular instance. Either way, authors do things for a reason, so when you encounter the use of a stereotype, seek to find the reason why you think the author has done it.