I find that in the first two generations, the games aren't exactly the most realistic. But as the games progress, so do links that tie in with real life, making it easier to relate to. RBY/GSC games are much too basic for an unimportant character. My favourite thing about RSE is the relationship with the father.
Then after that, I assume the people at Game Freak had problems with their own fathers instantaneously and therefore saw fit to rid them from the game. I think dads are due for a comeback if a Gen VI is on the cards though!
Or, alternatively...
I like the theory that Oak is Red's secret dad. It'd be very Star Wars-esque when Red battles his enemy; "Blue, I am your Uncle." And he seems like the sleazy type, but in a sort of ...loveable manner?
In GSC I used to pretend that the dad was the Dojo Master. Your mother met him when shopping in Kanto one day, he impressed her with his Karate skills and the rest is history. It was a one night stand, and when she discovered her pregnancy she travelled to Saffron to see he had disappeared, the Psychic Gym removing all his prestige and challengers.
When Gold finds him in Mt. Mortar, the Master is obviously unaware that he has a son. However, he recognises his child's features, and so he gives him a prize as a token for beating him and for the rekindled memories of a better time.
The mysteries shrouding Mr Pokemon and Mr Fuji spark interest in me also. Maybe our dear champion has Pokemon excellence running through his veins?