Running the place can be a poisoned chalice. The job has not often proved the means to enhance a reputation.
Little wonder that filling the post has previously been a protracted process. Finding a replacement for Tamara Ingram, who is departing to run WPP's global Procter & Gamble business, may prove to be no easier.
Grey's response in recent years has been to throw money at top talents who might not otherwise have given the agency the time of day. This policy can hardly be called an unqualified success. Indeed, it has led to some spectacular cultural mismatches and some unwelcome publicity.
The problem is not so much that the agency is broken. Indeed, its senior managers point to double-digit growth, which comes from an even mix of incremental and new business. It is more about how it should face the future.
Despite being absorbed into Sir Martin Sorrell's WPP, Grey is still the money-making machine its former boss, Ed Meyer, built on the back of a handful of multinational clients. Nothing wrong with that. Handling such complex business across a range of international markets requires extraordinary skills and are not to be belittled.
But times change. Bedrock Grey clients, such as P&G, are showing an ever greater unwillingness to accept bland creative work and to look beyond its agency roster to find it.
Meanwhile, there is the perpetual conundrum of balancing the portfolio with more national and regional clients who can be convinced they will not be suffocated by Grey's internationally aligned leviathans. Grey London has got to get better at this. Its failure to secure Sky's £75 million creative assignment is said to have had Sorrell seething.
Grey London's challenge is to keep its long-term customers happy, while presenting a compelling offering to potential new ones. And all of this while making sure the creative product moves steadily through the gears. Any takers?