I have hung out on HN for over 14 years and took a personal interest in "How in the heck did a pretty young woman co-found a company with three men,
date one of them and not have this turn into a
debacle and scandal in the headlines???" It took quite a few years for the details behind the founding of YC to come out:
1. Jessica Livingston did not co-found a company with three random men.
2. She and Paul Graham were dating, she was job hunting and being jerked around and he said one day "Why don't we start a company?"
3. Within a day or so, he called his two co-founders from Via Web and asked them to come on board like part time or something and they said "yes."
4. They initially hid their personal relationship as a dating couple to try to appear professional.
So they have a long history of being very private people and because I am a woman who has struggled to get any traction and blah blah blah, when I learned Sam was gay, I figured "Ah, that's probably the real reason he was appointed President of YC: Paul Graham wanted to protect his marriage while retiring from YC and was concerned about his pretty, younger wife working closely with a man other than himself. So he appointed a gay guy to take over 45 percent of his duties."*
So if that had anything to do with the hiring decision, not announcing the firing would be in line with long-standing personal policy to keep his private life private and not talk to the world about his marriage to Jessica Livingston and it wouldn't exactly be shocking if that meant it (hiring him) wasn't the wisest business move.
She eventually also retired from YC, so her being there while Paul Graham is home with the kids is no longer relevant to who runs things at YC. They are both founders and presumably major stock holders, I imagine they both still have influence there.
/"wild speculation" from an outsider who has never met any of these people but did sort of politely cyberstalk Jessica Livingston for some years trying to figure "How does a woman become a successful business founder?"
* "45 percent" because Paul said somewhere that he continued to do "office hours" with program participants and called that "10 percent" of what he did at YC before retiring. They also hired Dan Gackle to take over as moderator of Hacker News when Paul Graham stepped down.
So Paul was not replaced by Sam Altman. They hired two full-time employees that I know of and Paul continued to work part-time at the business while his wife worked full-time and presumably kept Paul up-to-date about daily goings-on over breakfast/dinner, so he likely continued to have significant influence on company decisions and day-to-day stuff invisibly via his wife.