As someone who doesn't do any of this, I think it's quite nice to look at portrait artwork. I have tried back in my childhood to draw faces, and if I recall correctly, the hardest parts would be getting the eyes to look just right. You could, for non-serious projects, get away with drawing a 2D nose, but weird and misaligned eyes seem to always ruin the drawings.
I'm not sure if this falls into the same category of drawing you're referring to, but I also think using a cartoonist's art style makes the portraits more easier to draw. They tend to exaggerate certain facial features a person has, and it's oddly easy to see the resemblance between drawing and reality. For more "quick sketches" applying this kind of formula may be wise.
Something like the Mona Lisa's style can be tricky I'd think. It'd definitely take a lot of practice to get into!