My peasants certainly don't.

I think one major step towards balancing the hero's would be giving them a salary.  A steep one that went up as they leveled.  That would force me to choose between a few elite units that eat my whole economy or many less uber but more affordable units (or worse keep me from building those studies all over).  Right now I pay 60-100 bucks for a level one hero and that's it for the whole game, hundreds of turns.  A militia made early in the game costs 1.2 gold per turn.  This adds up to hundreds and hundreds of dollars over the course of the game.  It just doesn't make economic sense and at the end of the day 4x games are a game of opportunity cost.  

I love being able to make uber powerful heroes but they should cost me in relation to their power.  As it stands now they have no downside and allow me to circumvent the rest of the game mechanics (who needs research!).