More than just sensor size
I'm no pro, but I do have a D70 which I got nearly 10 years ago now which I used (alongside several books) to teach myself the skills. Without doubt, the computing power in a modern phone is substantially better than the D70. Asides from the quality of the optical zoom (which you have limits of physics and substantial costs), modern point and shoot cameras and camera phones can take excellent photos. My big personal problem with them is that it is infeasibly slow to use any manual mode due to the fact you have got to go through menus for a few minutes to setup your shots.
If there was a way of getting a few more rocker switches so that you could quickly change the aperture (maybe limited possibility due to physics), shutter speed or dial in some EV compensation, it would definitely be an option for more than a look-at -me facebook post.
That and a proper flash would go a lot further to creating good photos than a gaizeeelion terapixel sensors. A physically large sensor with downsampling will go a long way towards ensuring that each recorded pixel is as close as possible to what comes through the lens. The real challenge is to ensure what comes through the lens is what you want.