The question of whether or not experts are harmful is certainly not a problem restricted to the game of chess.
An interesting question in the literature regarding the optimal design of Monetary Policy Committees (MPC) is whether or not committees should include outside experts who are not full-time employees of the central bank.
To put this into perspective, first consider the Bank of England's MPC. It is composed of five internal executive members of the bank and four outside experts. On the other hand, the Federal Reserve Bank employs a committee composed solely of bank employees.
Outside expert members are included in the Bank of England's MPC as they are believed to bring in expertise and extra information to that gained inside the Bank of England.
So, which MPC design is better? Experts in, or experts out?
Well, this area of research is still active and it has been investigated recently by Hansen & McMahon (2010). I suggest consulting the references mentioned in this paper for further reading on this issue of "committees of experts".
Is this a big (important) problem? Taking into consideration the effects that a MPC's decision may have for the economy, I'd say this is a pretty important problem!
Lastly, I ought to mention that monetary policy decisions can, in theory, be delegated to a computer. For example, the computer could be programmed to implement, say, a simple monetary policy rule; for instance, one of committment. This would remove expert input after the monetary policy rule has been programmed into the computer. The use of the computer in monetary policy is mentioned in Svensson (1999).
Stephen Eliot Hansen & Michael McMahon, 2010. "What do outside experts bring to a committee? Evidence from the Bank of England," Economics Working Papers 1238, Department of Economics and Business, Universitat Pompeu Fabra.
Lars E.O. Svensson, 1999. "How should monetary policy be conducted in an era of price stability?," Proceedings, Federal Reserve Bank of Kansas City, pages 195-259.