The Doge had no power.

Welcome to my rathole: Venetian history. To expand on your thesis, the Council of Ten was the executive power in Venice, but the Doge and minor council attended the Council of Ten meetings and the Doge often chaired those meetings. And even if he was powerless, the Council was made up of other old men. I don't want to push this whole argument, I'm not recommending we adopt the Venetian constitution. But I don't think you can blame current chaos on age.