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.

There is another variable, the rate of change. When a Venetian Doge was 80 years old, the world was.. more or less the same as when he was 20.

Contrast that to now, where an 80 year old in his twenties likely did not even have colour TV.

Can you explain how is the example of Venetian republic relevant for something like a massive multi-cultural, multi-racial federation in 21st century? One that's led by 100s of old people not just ten rich family heads?