The price argument is pretty interesting because most of the users here think that BOM and the retail price will be almost the same, but consoles that break even on launch day is a very new thing; except for Nintendo, the One and PS4 are the first consoles in my recent memory that actually break even on launch. Let's ignore the PS3 because its' development process was a cluster F and focus on the 360. When it launched, isupply estimated the BOM at 525$ while it was sold for 399$. That's a 126$ lose on every console sold, if you adjust it for inflation they've lost 164$ for every console sold in 2019 money. Sony lost more than double that per PS3 but that's a different story.
In 2013 something weird was going on in the console landscape and that thing was the Wii. Just like it got Microsoft to focus on the Kinect, the Wii also showed console makers that power doesn't matter that much and breaking even on the hardware day-one is actually doable so both Sony and Microsoft, for the first time ever, made consoles that cost less than they are sold for. But what did the past few years taught us, or more importantly what did it teach Microsoft? Microsoft saw how the XBO was crushed by the PS4, partially because of the power difference that made core players want the PS4 (both had terrible exclusives in the first year anyway). So Microsoft made the X and lo and behold, they are getting all the goodwill in the world.
So what if BOM and retail price are pretty far apart? What if losing 165$ on every console on launch day is worth it in order to get the user base that later buys games, LIVE Gold and Gamepass - just like they did every generation up until this one? We could see a 399$ console that cost 550$ to make, we can see a 499$ console that cost 650$ to make and we can also see a 299$ console that cost 450$ to make.
We don't know where Microsoft and Sony were aiming at three years ago when they made these decisions for the next generation. Sony might be aiming for a 399$ break even with a BOM ~400$ while Microsoft was aiming for a 500$ with a big lose with a BOM of 650$. It can also be the other way around, who knows? It's almost impossible to know. But you do have to keep it in mind when you say "there is no way X will have Y" when you might have a 250$ difference in BOM between the consoles.