There's a popular website used on the Xbox One that emulates older Nintendo consoles from within the included Edge browser with controller support, and it can use OneDrive to store your ROMs and saves.
Something similar to that on the Switch could eat into Virtual Console revenues.
A portable, dockable tablet with a built-in reliable controller? If it had a browser, I'd be surprised if people didn't specifically write some games to target it.
I'm hoping that they do bring it back, because Nintendo did see the potential and have dev tools for the WiiU to target html based content - https://developer.nintendo.com/tools
The 3DS used a relatively deficient browser engine, with much less support for web standards; it didn't support anything a non-trivial game might need.
A browser based on current WebKit or Blink, with full hardware-accelerated support for WebGL, a fast JavaScript JIT, WebAssembly, fullscreen, joysticks, and other such standards would make a compelling platform.
Well, the point stands: browser and integrated pad is not enough for third party browser games to emerge. Nintendo would also have to provide relevant APIs, some of which aren't commonly used by regular websites (e.g. WebGL).
