*quote from Wikipedia*
The fifth Labour of Heracles was to clean the Augean stables. This assignment was intended to be both humiliating (rather than impressive, as had the previous labours) and impossible, since the livestock were divinely healthy (immortal) and therefore produced an enormous quantity of dung. These stables had not been cleaned in over 30 years, and over 1,000 cattle lived there.
*end quote from Wikipedia*
If you are going for a totally realistic campaign then DnD really isn't the system for it. At high levels the skills can let the heros do things nobody in the "real world" can do without the aid of magic weapons or spells.
Such as...
1. Convincing a naked emperor he is wearing new clothes.
2. Convincing a dark lord of the sith to turn against his evil ways and regain his humanity (instead of just getting rid of him by slicing off his head).
3. Climbing a beanstalk all the way into the clouds without it breaking or you falling to your death.
4. Noticing a pea under multiples mattresses by feel alone.
5. Planting a forest of trees across the continental United States.
6. Becoming best buddies with a supremely powerful beast because you did him a minor favor he could have done himself (like say removing a thorn from his paw)
DS
Hercules is part god. That means he is a magical creature.
I have been playing DnD since it came out and I have never felt that I needed a different game to play the style of game that I want.
I am not a slave to totally realism in any game. But there are a few dealbreakers for me. Anything that starts feeling like something out of a anime or a superheros comic is one of those things.
I can accept Superman can fly so I don't have an issue with people using magic to fly but if you crash to earth and you don't have feather fall then unlike Superman you are going to get hurt even possibly die.
There is a lot you can't do in the real world because magic does not exist.
The Darth Vader example could be done with a highly talented negotiator. Vader as we know from his past was conflicted about what he became. So Luke had an opening to work with.
The emperor needing new clothes might be accomplished in game if you had a great bluff and the emperor had a wisdom score in the minuses.