Who should be responsible for monitoring and controlling strategic plans? Why?

I would disagree the control function is a management domain. The control function of management is the process of monitoring activities to ensure that they are being accomplished as planned and for correcting any significant deviations.  The control function ensures that activities are completed in ways that lead to the accomplishment of organizational goals. The control function also provides the organization with indications of how well the company is performing in relation to its goals. This indication can be seen through the comparison of standards to performance.  The control function also provides a mechanism for adjusting performance to keep organization focused on its plan and strategic objectives.