The Switch is a direct successor in a line of Nvidia tablets that were regularly priced at $200-$250. That being said, I'm not sure about its profit margin.
But I know for a fact that since launch the Xbone and PS4 were profitable. They were never sold as a loss leader.
Especially now, after all 3 have been out for years, none are losing money. They are all profitable when sold and then infinite money machines by acting as a tax on developers and consumers.
The NRE on consoles is pretty high, for the Nvidia tablets all the upfront costs of the OS have been fronted by Google and Nvidia hasn't been able to position their SoCs as a competitive processor given there have been almost no designs aside from their in-house products.
If wide open hardware and appstore was a recipe for success Android would be a clear winner. However if you want to ship a title where you get the most out of the platform and you can rely on the platform to be stable from both HW and SW perspective then curating that space seems to be a recipe for success.
It's be really neat if all the console hardware was wide open, however there's a bunch of hurdles there that tend to lead towards curated platforms being more successful.
But I know for a fact that since launch the Xbone and PS4 were profitable. They were never sold as a loss leader.
Especially now, after all 3 have been out for years, none are losing money. They are all profitable when sold and then infinite money machines by acting as a tax on developers and consumers.