Having worked in HR CoEs in many organizations, i have realized one cardinal mistake which companies do in anointing the leaders for the CoEs.
CoEs should always be led by specialists. Plain and simple. There is no 2 ways about it. People who dedicate many many years of their life first in struggling to get an opportunity in their field of interest and then sticking to that area through organizational and personal transitions, are best suited to lead the verticals. So for instance an L&OD professional or a C&B professional should be heading that particular vertical. They come in with a particular lens and see the organization through those glasses. They have a long term vision. They are then able to identify the gaps and the opportunity areas and then deliver benefit to the organisation.
Unfortunately, with the quality of HR Heads running the show going down day by day, hare brained ideas come into being. I mention deteriorating quality to signify that most have now stopped thinking and keep following what they have seen earlier in their careers. One of such ludicrous ideas is to consider the CoE head position as a transit role for gaining experience in that particular vertical so that HR professionals can become well rounded HR Heads. This is only a temporary stint for them. Without the wherewithal to lead the function, these are the people who do maximum damage to the credibility of the function. In such organisations, for years employees feel that nothing good is coming out of the HR CoEs. This is the sole reason and the earlier the CEO and Head HR understand that, the less damage will the CoEs and the organization need to bear.