Personally, I would put this responsibility on the shoulders of the project team and not the change control board. On every project that I managed, I saw it as our responsibility to review and assess change requests. Primarily because some of them can get pretty down into the technical details, which is knowledge that the decision makers often don't have.
Does the project manager (and project team) or the Change control board perform the analysis to determine how a change request impacts all the project constraints? It's my understanding the analysis should be done prior to submitting the change request and coupled with several proposed corrective/preventive actions?