The reason why the Switch has blown up so much is convenience. On paper, the Switch falls short in almost every category. It's not as possible, its games don't perform as well, and it doesn't get nearly as many cross-platform titles. In theory, it should be no different from the Wii U, relying solely on its first-party developed Nintendo titles.
But Nintendo went all-in on the portability, and that ended up making the difference. They also took notes from the Wii U, and stripped the interface down to the bare essentials to insure that they could get it running extremely fast. At pretty much every point, they sanded the edges of the Switch down to make it as convenient as possible. And that was enough to make the difference. An easy, quick, convenient portable system with a solid digital library, cheap digital storage, and the ability to pop it on and off of your TV. That turned out to be the winning formula.
Nintendo also benefited from the boom in smaller-scale indie development. If not for the indie scene exploding, the Switch would be far more starved for content. High-end graphics heavy titles like Call of Duty don't work well on a much more modest system like the Switch. But lower-requirement indie titles with more modest graphics fit like a charm, and frequently pair well with gaming-on-the-go. As ever seems to be the case in this industry, success boils down to a combination of good choices, and sheer dumb luck.