I don't know if they've ever directly addressed it, but I think this actually is the reason.
Thinking about the timeline of the show... Kendall just turned 40, and assume Shiv and Roman are supposed to be a few years younger, which means that Logan was initially with their mother at least 40 years ago, if not a few years prior; so that would probably have put Conner in his late teens or early 20s (at the oldest) when Logan and his mother split up... (assuming that Conner is supposed to be in his early 60s in the show...Alan Ruck is 66 IRL).
We know that Logan was with Kendall/Roman/Shiv's mother until Shiv was 14 (?)...(it was mentioned last season, can't recall exactly)... so Logan was likely completely focused on his "new" family essentially for the entirety of Conner's 20s and maybe into his early 30s.
So the likely situation is that Logan basically sent him and his mother on their merry way with a big payoff and either Conner never had any interest in joining the business or Logan had no interest in "inviting him" since he was focused on his "new" family at the point in Conner's life when he would have otherwise joined the business.
I think the idea was that, knowing Menkan's fascist tendencies, he would basically declare himself the winner as soon as a reputable network declared the win, which is exactly what he did. Does that mean he DID win or was the TRUE winner? Indeterminate. But being the good fascist, he was certainly going to declare himself the winner and imperil democracy, as Shiv predicted he would.
And I think the point was to show that, YES, just a few people sitting in a room making calls CAN "decide" these things.