Holmgren can stay where he is, as far as I'm concerned.
I respect him as a coach, but have several issues with him:
1) The infamous Superbowl-leaving-for-Seattle business. It distracted from the team's accomplishments and was the first hint of Holmgren's ego being a little larger than was previously known.
2) Holmgren's "legacy" - he coached well, and he helped to develop Favre, but Favre is also a natural talent and a franchise player any team in the NFL would have dreamed about. Did Holmgren win that (one) Superbowl, or did Favre? Did Holmgren make the Pack an NFC force in just a couple of years, or did Favre? You make the call. Favre did thrive in the West Coast offense, but chances are he would have thrived anywhere.
3) Holmgren's demands in Seattle. Just one more of the "I want total control" superego coaches. He demanded to be coach and GM until Seattle was so sick of him, they were about to run him out of town. He had to concede the GM position in order to keep his job three or four years ago. Since then, things really turned around for Seattle, obviously, but giving Holmgren total control at the outset really exposed him for not being the football genius he projected.
4) speaking of being run out of town, his hard line with several Seattle players never sat well with me, and he sent Joey Galloway packing and really hurt his career. Galloway had been one of Seattle's superstars (of which they had very few at the time) and if I recall, was trying to renegotiate and Holmgren very publicly did not budge an inch, exerted his "power" and Galloway sat until he was forced to go elsewhere. Not cool, at least my impression of it. He also got rid of Ahman Green - much to our pleasure, subsequently.
I don't dislike Holmgren and he has come a long way towards being more concilliatory, and diminishing his ego a bit. But it took several hard seasons in Seattle to get to that point. Looking at them now, it's easy to forget they really struggled for the first several years he was there.