But why would Ilya publicly say he regrets his decision and wants Sam to come back. You think his existential worries are less important than being liked by his coworkers??
Yes, actually. This is overwhelmingly true for most people. At the end of the day, we all fear being alone. I imagine that fear is, at least in part, what drives these kinds of long-term "existential worries," the fear of a universe without other people in it, but now Ilya is facing the much more immediate threat of social ostracism with significantly higher certainty and decidedly within his own lifetime. Emotionally, that must take precedence.
His existential worries are less important than OpenAI existing, and him having something to work on and worry about.
In fact, Ilya may have worried more about the continued existence of OpenAI than Sam after he was fired, which looked instantly like a: "I am taking my ball and going home to Microsoft.". If Sam cared so much about OpenAI, he could have quietly accepted his resignation and help find a replacement.
Also, Anna Brockman had a meeting with Ilya where she cried and pleaded. Even though he stands by his decision, he may ultimately still regret it, and the hurt and damage it caused.