I know what you mean, but Nintendo is a pretty bad example to illustrate that sentiment. I mean, they totally do corporate crap to benefit them and not the players obviously, but the Zelda series is literally built around the gimmicks of the console. They start thinking about a gimmick, either on the console and / or how to turn that into a gameplay gimmick, and then they make a Zelda game around that. OoT had the rumble pack and then tried to do Ura Zelda that was supposed to be the system seller for the DD64 - but that blew up and was salvaged between Master Mode and Majora's Mask. The GameCube had Four Swords with the connection to the GBA and the multiplayer. The Wii had Skyward Sword with the motion thing, the Wii U had the separate tablet. The DS then the 3DS weren't too relevant for Zelda but they tried, and other games did rely on it.

I'm not saying it's a fact for the whole series, but Nintendo is particularly famous for developing a gimmick console and then building games around that, so yes, the physical console is actually relevant to the game you want to play it on, you'd be hard pressed to port that elsewhere and emulators are always weird and have a lot of work to adapt into something that makes sense on a single screen with a basic gamepad.