I think there is a rare chance that Sony, and Nintendo may someday release a cheaper gaming handheld console without a built-in controller where users would have the option of using touchscreen controls and motion controls built-into the device like phones, buying the official standalone controller for a handheld console, or using their own controller from a PS4, PS3, Wii, or PC.
But, I feel most handheld game console will still come with built-in controls unless there are many gamers in the future who rather use their own controller while playing handheld games, or there are a lot of gamers who are fine with buying a cheaper handheld without a controller to save around $50 or less by buying a handheld without a built-in controller.
I bet, Sony could release a touchscreen-only handheld console which runs Google Android, or Sony can release a Playstation-branded Android smartphone or tablet designed mostly for Gaming.
I read on a tech blog Sony wants to publish more of their Playstation games to Google Android for mobile gamers to buy because of the success of mobile games like Pokemon Go which makes millions of dollars a day.
Most Playstation Android games will most likely work with Sony's PS3-PS4 or regular controller with the same button layout as the Playstation controller, so gamers can use their own controller to game with instead of paying more money for a handheld with a built-in controller which they may not want to use because a full-size PS3-PS4 controller is more comfortable to use for long periods of time, and they rather use a controller which they already own.
As it stands right now, I still prefer to have the handheld with the built in controls.
With the way that technology changes over the years, who knows what they will come up with in the future. They could always make something newer and better versus what's already out there. Technology is something that is constantly evolving. With that in mind, if they come up with something that I may like more.
I think a wiimote or those Clone/knock-off Nintendo or SNES wireless controllers are easier to carry around because they are smaller than most modern smartphones.
I usually carry a bag when I go out, so carrying around a controller is not inconvenient for me.