So your "Switch 3" idea is sorta similar to an idea I had for their next system (so "Switch 2"). Basicly it's just a handheld and instead of a dock you have a HDMI reciever that you can plug into any TV or monitor and then stream to it from the console. Like you said it makes it easier to not only take your Switch with you anywhere, but also play it on any screen.
In addition, since the console doesn't have to be plugged into the TV it would allow for the console itself to be used as the controller, certain games could even utilize the console screen while playing on the TV, Wii U style, like for example Mario Maker where its awfully convenient for making courses. Though of course this should only be an optional way to play and preferably the console should still have detachable joy-cons, especially since you can't really have the console plugged in for charging while you're using the whole thing as a controller.
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