To your point, it was briefly possible to buy them for under $100 until word spread that they make decent steam machines, so I'm guessing that Sony doesn't need to sell any games to turn a profit. Even at their current prices it would be far cheaper to use the BC-250 for local inference.
I don't follow your logic. If the BC-250 was made from PS5 quality control failures, then why would their pricing have any bearing on the PS5's profitability, except as an effort to increase margins? Does cost not remain independent of pricing?
As far as I cam infer from what you said, it could be that the PS5 was sold at a loss and still is even with the BC-250 helping, or that it was sold at a profit and is still is with the BC-250 helping. What am I missing?
The only way they can lose money is if their existing users stop buying games and that's not happening yet. Maybe when vibe coded community servers for online games get better and everyone jailbreaks their console because they don't have to worry about getting banned.
But even with that every unit sold is a net positive for them because they make money off the sale, and if they run out they can use it to justify higher prices.