Depending on how you play doges are not necessarily that dangerous to use. Generally, they become comparatively more effecient the higher the crown autority you normally operate with.
Doges have no opinion malus from crown authority but are still required to provide levies as per the level of crown authority, so you can gain a bit of favor with them by lowering the percentage of levies they are required to provide without actually loosing access to those troops.
Examples:
high crown law, max levies, no tax from feudal; min levies, max tax from doges = -25 malus, 0% tax, 100(60)% levies with feudal ; -40 malus, 45% tax, 60% levies from doges.
Increasing the feudal tax or decreasing the city tax by 10% would put feudals and doges almost on par in this case (-35;-40 or -25;-30).
Absolute crown law, max levies, no tax from feudal; min levies, max tax from doges = -35 malus, 0% tax, 100(80)% levies from feudal ; -40 malus, 45% tax, 80% levies from doges.
Increasing the feudal tax or decreasing the city tax by 10% would make doges compatively more attractive in this case (-45;40 or -35;-30).
In short, unless you operate with medium or lower crown authority then using doges is not materially more dangerous than than taxing the nobles. Keep in mind that there is no rule that force you to always use harsh city tax, if doges become a problem during transition of power you can always lower the tax and then raise it again later! Moreover having a handful of doges will provide you with staggering sums of cash that can be used to ensure the undying love and loyalty of all your noble vasals.
Doges have no opinion malus from crown authority but are still required to provide levies as per the level of crown authority, so you can gain a bit of favor with them by lowering the percentage of levies they are required to provide without actually loosing access to those troops.
Examples:
high crown law, max levies, no tax from feudal; min levies, max tax from doges = -25 malus, 0% tax, 100(60)% levies with feudal ; -40 malus, 45% tax, 60% levies from doges.
Increasing the feudal tax or decreasing the city tax by 10% would put feudals and doges almost on par in this case (-35;-40 or -25;-30).
Absolute crown law, max levies, no tax from feudal; min levies, max tax from doges = -35 malus, 0% tax, 100(80)% levies from feudal ; -40 malus, 45% tax, 80% levies from doges.
Increasing the feudal tax or decreasing the city tax by 10% would make doges compatively more attractive in this case (-45;40 or -35;-30).
In short, unless you operate with medium or lower crown authority then using doges is not materially more dangerous than than taxing the nobles. Keep in mind that there is no rule that force you to always use harsh city tax, if doges become a problem during transition of power you can always lower the tax and then raise it again later! Moreover having a handful of doges will provide you with staggering sums of cash that can be used to ensure the undying love and loyalty of all your noble vasals.