Should we hide the CEO?

Earlier this year I attended a small VC event at which Jim Collins was giving his fantastic presentation on how to build great and enduring businesses. He did a marvelous job of both reminding the CEOs present of the management disciplines they need to adopt if they are to turn their businesses in to truly great companies. Several months have passed since I heard him speak but I was reminded of this speech when I noticed his 'Level 5 Leadership' article is being reprinted in the current HBR. What struck me is that if you look at the current leaders of the major tech players there is some correlation with his central thesis, that great companies have Level 5 leaders but not a complete correlation. Of course this could be a warning bell for the future of those that don't appear to have Level 5 leaders, or it could be that Jim's analysis doesn't really apply to them.

Jim's research suggests that Level 5 leaders have a common set of traits, namely their ability to build enduring greatness through a paradoxical combination of personal humility plus professional will. Now I can't profess to know the CEOs of the all the major tech firms to the extent where my judgment is 100% accurate but from what I've learned over the years and from the insight others have given, I'd say that using media exposure as a guide the following people meet the Level 5 standard:

Sam Palmisano - IBM. Sam does work with the media but it's clear that he'd rather talk about his company than himself.
Mark Hurd - HP. Has any business publication managed to profile him with his involvement?
Hector Ruiz - AMD. AMD has been slowly but surely gaining ground on Intel while Hector has stayed firmly below the radar
Bill Gates - Microsoft (I know he's not CEO anymore!). Bill has never loved media attention but accepts its role. As the world's richest man he can't escape being on the cover of magazines from time to time
Steve Ballmer - Microsoft. Steve may be gregarious but he's also not someone to blow his own trumpet.
Paul Otellini - Intel. Since taking over as CEO he has hardly sought out personal publicity

Some may take issue with these choices and I should add that not that all of these are clients. I should add that I've not included CEOs such as Steve Jobs, John Chambers, Larry Ellison and Scott McNealy. I don't know these people but the perception is that these people enjoy the media spotlight which goes against them being so called Level 5 leaders. If my perception is wrong then these guys all definitely count. It is interesting to note that Jim's Level 5 criteria if used when hiring CEOs would have ruled out hiring someone like Carly Fiorina for the HP role.

If you think about this you arrive at something of a paradox. At one level PR people want their CEOs to do their part to raise awareness of the company and its goals. This often means them sharing some of their personal life with the public to add some human interest to an otherwise dull business story. If they do this too much then they become celebrity CEOs and by Jim's definition, this would suggest they are falling short of being Level 5 leaders. So the logical conclusion you arrive at is that we can do all our clients a favor and make sure our CEOs stay out of the media.

Or should we? I'd love to see what other PR people think on this subject?