The flaw in your argument is that you are saying it's designed as a $200 dollar machine and yet the BOM is higher then 300. That is without taking into account warehousing, shipping, packaging and so on. It screams as being designed for the $300 price point, it's already selling at a pretty nice loss. They can only get close to the $200 price point by moving to a lower fab node, which isn't cheap, btw.
The other flaw in your argument is that the PS4 has sold over 115 million units with the majority of them at around the $300 price point, which hey, look at that, that's the price point the Series S is designed for. Funny huh?
You still haven't replied to the point about the actual state of the market, where literally everything decent is sold out. CPUs, GPUs, PS5, you name it. Yet the Series S can be bought right away, no issues, everywhere.
I'm not saying it's already failed, I'm not Nostradamus, but given the original plans to have a mass market device, not selling all that well, in this market...let's just say it doesn't look pretty. It's like a bunch of people dying of hunger refusing to buy a tuna sandwich because everything else in the store is sold out and just prefer to wait until the chicken or beef sandwiches come back.