I agree with your sentiments. Perhaps it's because I didn't grow up with touchscreens, but I find the controls on anything but the simplest games to be less intuitive on mobile than on a handheld device. It isn't that bad when you just need to tap somewhere, but when it comes to interacting with a control for any length of time, I much prefer to use a physical one rather than a virtual one. Holding B to sprint, or moving the directional pad or joystick quickly, works much better in the physical world. Perhaps phones are much better as gaming platforms than the typical UX design gives them credit for, but I can't imagine a phone replacing the sheer joy my Gameboy Color brought me when I was 8. I mean, the LCD on those things absolutely sucked, and being able to charge your battery is awesome, but a Gameboy is a complete experience. Nintendo is more Apple than PC -- that is to say Nintendo makes a complete product, where the design of the hardware plays as much in to the experience as the software.
For instance, one of the most common complaints with Pokemon GO is that the game monopolizes your phone while you play it. You have to have the game running in the foreground of your phone with the screen on at all times. If you switch to take a call, or you switch to play some music, or use your GPS, or whatever, the game stops tracking your progress. By designing separate hardware, Nintendo is free to make decisions like that without upsetting people who (rightfully) expect apps to be able to share space on their phone. It's easy to compare Nintendo consoles to those produced by Sony and Microsoft and determine that Nintendo is losing the war, but in the end, Nintendo is creating an entire experience. Their methods are sometimes questionable (I'm looking at you, new Star Fox), but unlike Sony or Microsoft, they have created an ecosystem that depends on the unique features of their systems. The reasons I'd purchase a PS4 or a Xbone are 1) I want a platform exclusive game 2) I want to play with my friends who have the same console or 3) I want to be able to play multiplayer games more easily than I can on my PC. There is nothing on this list that a PC couldn't do if given the chance.
On the other hand, Nintendo has done a lot of cool things with the Wii U. The wiimote and nunchuck actually works pretty well now that I've gotten used to it, and their platform exclusives use their hardware really well. I hung out with my 6 year old cousin all day on his birthday and played splatoon, which is a ton of fun, and makes really good use of the game pad and screen. The game pad is pretty sweet in general. Being able to play a game while other people are using the TV is pretty sweet. My friends and I will sit around watching sports, while one person builds a custom level for us to play in Smash Bros. Plus, it solves the issue of LAN Hacking, and allows one player to have information the other players can't see, which has been used to good effect in a few games and definitely has a lot of potential.
Regardless, I think claims that this is the last generation of console-specific hardware are exaggerated in general. I think Sony, Microsoft and Nintendo will still be producing consoles in ten years, just because the simplicity of a gaming appliance will always be appealing to people. Ensuring a phone or a computer is properly set up and specced to run a game will always be more than a large number of people want to deal with, especially as we get in to new technologies like VR and AR.