SAQ have practical problems for the faculty , for example Marking, defense of the model answer , ability to frame and validly assess.
SAQs Questions requires very careful consideration to make it specific and narrow it down to one or two possible answer. If not carefully written and there are possible 10 answers then it defeats the purpose.
Agree with Mutaz Alhasien comments and also require large number of examiners to mark them. For example for our SAQ exam we needed 50 examiner each day for two days to mark 900 papers.