Why can't problem groups be used in regular homework assignments. I this something that may change in the future?
It has to do with the way gateway quizzes are stored in the database.
This has been brought up numerous times, and it is a desired feature, but making it work properly with regular homework sets would require some significant modifications to the code that no one has been willing to take on.
You can take a look at http://webwork.maa.org/moodle/mod/forum/discuss.php?d=3651&parent=9783 which describes a way to do this in homework sets. I have used that in the past, and it worked for me, though I haven't tried it in the latest versions. IIRC the idea was to permute the order of the questions, so if you use this to choose one question from a set, you have to make sure the question number in the assignment is less than the number of questions in the collection it is drawn from (i.e. if you are using this to choose a question from a set of 5, you can't make it #6 in your assignment).