This is more of a trivial fact then headcanon but related nevertheless. I don't believe I have enough posts for linking to the source but Google is always there for you. Hopefully you can just take my word for it.
As we all know SNES came before GB/GBC. Hopefully that common sense. Earthbound (Mother 2) was a SNES RPG that they wanted to try to sell in the US so badly that they even include a guide in the giant box that it came in.
Ok, one of the things that inspired the guy who made Earthbound was The Body which the short story Stand By Me was based on.
On Pokemon G/R/B/Y (pretty sure it was on Yellow as well) the TV in your house have a scene from Stand By Me.
Sure, it could just be a totally random reference but it could also been a way for Pokemon show reference from Earthbound. You could also just type the two simple keywords "Pokemon Earthbound" into Google to find other stuff that people think are references from Earthbound, some less believable while others like Pokemon naming their towns after colors like how Earthbound name theirs by numbers (Fourside) are more so.
Worth pointing out that Ness didn't really have a father at home, love to ride bikes and lastly he wear a cap.
Basically, the fact could be simply because Ness didn't had one, Red doesn't get one either. It could just by a copypasta design choice.
Now back to the fun discussion of headcanon. My favorites are currently:
1. He died in a war.
2. Team Rocket Boss is him. Explain why his gym was right next to his town.
3. The guy who help you in Brock's gym was your father too scared to tell you so. He travel gym to gym to help you out which explains why the gyms allow such a guy...He shouldn't be there!