Dynasty was a game in the game, and as that it was fairly hard to really let it interconnect with the rest of the game. The only interest was for new heroes.
So, for an interesting dynasty system it needs to use a lot of the actual system : create connection with the stat system, with the magic, with the research, with cities, with armies, etc.
For instance : when a child is born you can choose a "path" for him (I mean what will you teach him/her):
Path of the hero : when it will reach adulthood, your kid will become a level 1 hero. If he/she don't die before due to poor conditions and training (for instance ona 50% the kid dies, 30% it starts with a wound, 10% it starts good, 10% it starts at level 2)
Path of the governor : you don't get one more hero, but you "attach" your kid to a city providing some bonuses. One governor per city, and you can level up the governor.
Path of the magi : You "attach" your kid to magical research : every 10 turns you have a 10% chance to get a new spell, or mana, or etc.
Path of the merchant : you "attach" your kid to a city : it generates more gold and you can have 1 more road
Path of the diplomat : you "attach" your kid to an oppponent and you can gain some intel on them, you get a better view of treaties, etc.
Path of the healer : you "attach it to an army, that army gets +X health per turn, and the army can revive land if they stay (so you can create good places for new cities)
etc.