He seems to be mixing some terms a little bit. Correcting distortion lowers sharpness -- though for any image displayed only at 1080p, it probably makes no difference. Correcting some other aberrations, like chromatic aberration (CA) lowers contrast (and sharpness). Higher sensitivity in a digital sensor lowers contrast a whole lot more, though. That, and poorly-controlled lens flare, usually the major driver of low-contrast images out of smartphones. If you take a picture in daylight, don't point it right at the sun, and have a clean lens, the picture comes out pretty good.
I don't have a good sense as to how good the smartphone lenses are now. But people are now making pancake lenses for interchangeable-lens cameras that are tiny and of very high quality. I suspect that it's not to hard to engineer good smartphone lenses, either.
The problem is that with such a small sensor, you need very bright lenses to get shallow depth of field or good low-light performance, and those are just plain hard to make.