The problem with electing (human) agents is that you suddenly have principle-agent problems. Their priorities change if they gain status from being selected, whether it's because they want to be re-selected, or because their time in power is limited, or because it is unlimited. If they don't gain anything by being selected, you are likely to have no incentive for them to invest in making optimal decisions.

Even if this is untrue, you need to project their decisions, typically by assuming you know something about their utility; if this projection is mis-specified even a bit, the difference can be catastrophic; their utility also may not be stationary. So their are some issues there, but they are interesting ones.