Ideally, totally forgotten about, like in say Star Trek where they carry gadgets around and barely any "Flat" or "recharge" type discussions. I never see a cable.
Ideally therefore you're carrying a device and it simply never needs recharging, the internal battery needs and its recharging is a non-issue, forgotten about, like Oxygen is taken for granted in every place which isn't sealed from the outside.
To do this truly seamlessly would involve wireless transfer to be pervasive but under current physics that's a challenge as electromagnetic power drops to the square of distance. So you're talking an awful lot of different technologies converging, like robotic controlled lasers who track you and point energy at you as you move (without blinding you or you noticing).
We need more wireless charging phones built-in, but that never really happened and metal cases in new phones are defeating the idea. I not bought a wireless charging device since about 2014.
Another is wireless mats built into many more places like office desks, bedside cabinets, kitchen surfaces, etc.
To survive the time between these yet-to-be-invented pervasive wireless recharging, we'd need phone batteries to last days, ideally weeks, which would require a substantial internal gadget battery density to go up at least one order of magnitude.
However, back to the right now, I never get a flat phone or tablet and stuck waiting, because I always carry something to get me out of the problem, if I'm moving for more than a day I'm usually with some kind of Anker Powercore. So really, all that this new wondrous technology will likely solve for me is remembering to pack a few items which are charged, which isn't that much of a burden as I must also pack food+water+clothing and unless Anker is planning on making us immortal also then energy for our gadgets is a subset of energy for our bodies.
I mean, a Powercore 10000 + cable is about the size of a palm of my hand and gets me to 2 days of phone life, it's hardly that bad now is it?