When you get the gold mine event, you can choose between:
1. Ignore it, and let another hero find the mine
2. Destroy it, and get ruthlessness
3. Donate it to the city, and give your society +10g/turn
4. Keep it, and get the filthy-rich modifier. Which gives you stat boosts.
The best option currently is #3. I have no idea what being ruthless gives you in the game, or what it might in the future. The problem with choice #4 is that... heroes die.
So, why not make the gold mine inheritable? When the hero owning it dies, give it (and the filthy-rich modifier) to the eldest surviving child. Or maybe chose between the children. If they have no children, then it reverts to the state and you get the +10g/turn.