I'd argue the incentives of elected government and private citizens are even more misaligned than "private" ones.
Elected government official doesn't own or have perpetual interest. All he can do is plunder as fast as he can in his unowned fiefdom before it passes on to the next guy. Fully private government would have incentive at least to preserve the value of the "Kingdom" if nothing else for his own children and because he sees the Kingdom as his own and destroying it for short term gain would be irrational.
But then you have the tragedy of the commons. As a central dictator, yes you want to preserve your government, and you act in ways that do this because you are the direct owner.
But in a democracy where you are one government official among many many other officials, one small corruption change that benefits yourself individually hardly effects the overall government. It is rational for you to do small damage to the overall government and gain a reward that benefits you disproportionally. It is the MOST logical action.
But then every government official acting rationally in aggregate causes the overall government to become extremely corrupt and that is the tragedy of the commons. Rational action in aggregate becomes irrational. Government needs to be separate from private business.
I guess it's because it's so culturally ingrained that it's hard to separate. The chase for money and business is entirely cultural. Money is paper and it's all fantasy stuff and the reason why we value it is solely because of culture. Government ideally needs to be seperate from this culture and have a more militaristic based honor structure where the incentive is to guard the citizenry. Government needs it's own cultural values. Easier said than done, practically every government official IS a private citizen and they all face the same misaligned incentives.