In addition to the other explanations offered, it was stated that many of the people wearing those costumes were not really actors, but well-known fans (ie. Bjo Trimble) or authors such as David Gerrold. These people were given a small part in the movie as a "thank you" for their years of support.
As to why nobody else ever wore those costumes... maybe they were constructed to fit a particular person?
It's also possible that the costumes weren't up to snuff for any lengthy screen-time duration. From what little I've seen of those masks, they make the Antican And Selay masks from The Next Generation
look life-like and flexible by comparison.