I don't know about Xbox dashboard but it certainly makes a huge difference in Windows desktop and in smartphones for me and many others.
That's not how it works. Input lag of every device in the chain adds up so it's controller input lag + console/game engine + display.
My LG Oled from 2016 doesn't support black frame insertion but in those TVs that do can they even use it in game mode.? Doesn't that increase input lag as it is additional processing.?
personally I don't like BFI. Yes it adds extra input lag and even worse, it makes the screen half as bright