Hardly. PC gaming was big before the Xbox and one could argue that the platform would be actually better off without it: a lot of PC games are shitty console ports or just crippled in general because the low-end hardware of these consoles.
And the "next-generation" doesn't look better either. Console hardware is already outdated right out of the gate, the second half of their generation will be painful.
"I rather use C++ than being stuck in .NET 3.5, without any more modern C# goodies" - I use all modern C# features with XNA - what is the issue (except for async/await maybe)?
"I guess one has to decide if they want to make a game or a game engine" - exactly, but there should be a choice. XNA being a framework rather than engine provided such a choice in a high-level way.
> Regardless how much XNA was praised, it was a indie only thing.
The majority of professional studios still use C++ based engines.
Unity is the Microsoft's endorsed replacement for XNA, as announced in the Visual Studio 2013 release keynote.
Doesn't matter. Goodwill is important, Microsoft is big enough they can afford to maintain 1 library.