I don't think it's too unreasonable to expect the minister for health, say, to have had a successful career working as a doctor in a hospital before entering politics, for the chancellor to have succeeded in business, for the defence minister to be a decorated soldier, etc etc.
There are numerous examples of politicians who have the matching formal education but make horrible politics irregardless. Here in Germany the minister of health was a physician and despite that he mostly was a lobbyist for the pharma industry (among other wrongdoings) and many of his decisions actually worsened the situation of regular patients. We also had lawyers in the ministry of justice who without blinking an eye issued laws which later were proven illegal by the high court.
From a politician I expect a clear political vision and use expert knowledge to find the best way to achieve these goals. The necessary expertise can be acquired by, uh, experts which has to be done most often anyway as the minister himself does not usually have the time or specialization to deal with specific complex issues. What I expect from a minister though is to make a wise selection of experts he draws knowledge from and still make the final call whether he will follow the recommendations.
