Too much discovery learning will bog everything down. I have not noticed any. Once in a while, you get students who want to work only alone. Sometimes students, especially weak ones, are too accepting of others incorrect thinking. Being exposed to this degree of error or inelegance may not have occurred in a non cooperation environment.
Some students think it is a waste of time.
They think they learn the subject the best by doing their own work, and focus on what they are assigned to do. Integrating group learning, activities, projects and computer technology can be overwhelmed. Students complain the structure is not as organized as they expect. None I don't think I have noticed any decline in the skill or the learning of mathematics as a result of group learning. My only problem is dealing with occasional dysfunctional groups effectively.