The lack of a web browser is I suspect a reaction to WebKit vulnerabilities having been one of the primary entry points for people hacking the (New) 3DS. Omitting this functionality reduces the OS's attack surface.
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.
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.
Something similar to that on the Switch could eat into Virtual Console revenues.
My bet is that they felt they needed more time to figure out how to properly sandbox it to prevent homebrew/piracy-related exploits, and that it will be released as a free installable item (or packaged with an OS update) in the next few months.