None, to me, outweigh the value of science fairs. Some people feel that science fairs have become too bureaucratic. Forms must be filled out and guidelines adhered to that sometimes seem unnecessary. But, like it or not, following rules is part of the scientific process. Sometimes non-science teachers in a school are part of the problem.
Some teachers seem to feel that the science curriculum intrudes on their own courses.
Some even resent that the science fair gets more attention than their area of interest. Another reason a science fair might be troublesome for a school's administration is the possibility that controversy will rear its ugly head. Suppose Kansas decided that a student's science fair report should not mention evolution, yet a parent who understood the importance of teaching evolution insisted that the child include it. Some school principals might decide that the easiest way to avoid the potential conflict would be to no longer have a science fair. Ironically, in this context concerns about overinvolvement outweigh those of no involvement.