Both of those situations were nothing like the situation in Carolina
I've said this before: new GM != new coaching staffs. The Giants and Eagles both changes GMs without changing coaches.
First off both of those GMs left of their own accord
1 Accorsi retired and Heckert left to take the GM position in cleveland (most likely because he was truly only and advisor to Andy Reid in Philly not a full GM)
2 Both of the coaches in the example had been to the playoffs 2 years in a row at the point of the new GM being hired
3 The GM in Philly likely doesn't have the authority to fire the HC as Andy reid is the executive vice president of football operations in philly and has the final say on all football related moves (he is the GM for all intents and purposes and the GM in title is his assistant)