They don't do anything. Dynasties in WoM don't matter in the slightest to how the game plays. Fundamentally all it really does is provide a way to farm a good champion up. You could axe it and it wouldn't really change the game.
The "dedicated team" is busy improving more important things (like cities, tactical combat, and magic). When you have limited resources you need to devote them to where they'll do the most good, and figuring out how to make dynasties into a core game element is a lot less important then improving the actual core game elements.
I'd like to see the concept come back at some point, but only when the resources exist to do it well. There's a lot of stuff like this in WoM where "less is more".