Using that logic, BOTW should render on TV at 1080p 60 FPS and be able to render on the gamepad at it's native resolution as well. BOTW isn't Smash. BOTW is a large open world game, Smash is confined to small stages with relatively little going on in comparison. Tekken 5 was 1080p on PS3. Why wasn't The Last of Us also 1080p?
BOTW demands a lot more of the system than Smash does, you're going to have to accept that some day. BOTW doesn't even hold it's 720p resolution, dipping down as low as 544p. It doesn't hold its 30 FPS, dipping into the teens despite that dynamic resolution. BOTW is pushing the WiiU to it's limits, hell it's one of the only Nintendo made games on both WiiU and Switch that isn't 1080p on the Switch. It's not a matter of just the second screen, it's rendering everything it is rendering for the TV to the point that it can't hold it's resolution or frame rate and rendering the game pad as well.
I mean, you might have had a better point asking why WWHD and TPHD, also Zelda games, are 1080p and output inventory to the gamepad. But even then those games aren't nearly the size of BOTW. All of Twilight Princess is the size of the Great Plateau. It's about the size of the assets in memory, how many of them there are, draw distances, and the like as well. It's not as simple as "but 1080p!".