I see no major issues with an elected official also serving as Head Banker, other than the time commitment of the person involved.
The concept of fake money in this roleplay introduces the potential for unjust favoritism or, more simply, negligent management and those sorts of things.
An abuse of either position may be handled the usual way - through impeachment. Or, because we all know the impeachment process is broken, through a recall election, assuming we get that bill done.