Hi Stephanie

It is possible to go into each of the competencies you don't want to be available for self assignment and under Non-admin assignment availability untick the Users who may self assign checkbox

The button Assign competencies still shows but only competencies with the self assignment ticked will be available for selection.

If you are wanting no competencies to be self assigned then edit a common role such as the authenticated user and untick the Capability Assign competency to yourself - this option hides the self assignment button 

regards