Local political machines not wanting to outsource control to city councils or technocratic "city managers".
What would happen if a city switches to a system with a city manager?
City managers are the top administrative officials in municipal governments, but they are not elected nor do they have a vote on the city council. While some mayor-council governments have appointed "Chief Administrative Officers" with responsibilities somewhat like that of a city manager, city managers have more discretion and independent authority (typically set out in a charter or some other body of codified law).