I have a wookiee, a sentient spaceship, a sentient crystal, three human Mandalorians, and two near-human Imperials. At one time I had a Yammosk PC and two clones as well.
The problem with non-human characters is that the design concept people tend to come up with for them is fairly narrow, which makes them hard to write. Compound that with a most canon races having a very narrow cultural background to pull from (such as Zeltrons being hookers, Twi'leks being strippers, Duros being... Creepy, Hutts being sleazy, exc) and you end up feeling trapped in a very narrow box trying to write a non-human in Star Wars. Then there is the language aspect, which is a nightmare to write sometimes, and the problem with trying to be easy to understand and fair to write against in competitive threads... Most non-human characters just... End up sat on a shelf in favor of simpler, more flexible human characters.