A couple of comments:
Putting the nut (as a whole) just very slightly closer to the 1st fret than the pure math would indicate, does help with intonation. It's easier to visualize this if you don't think of it as the nut being moved closer, but rather that the nut is where it's supposed to be, and ALL of the frets are moved just slightly closer to the nut. (Of course, the two are really the same...) The open string is tuned correctly (by definition). Then, by having ALL of the frets moved slightly closer to the nut than the pure math would indicate, the pressure applied on the string to fret any of the fretted notes is compensated for (on average).
In a true compensated nut, the adjustment is very slightly different for the different strings, since the different strings react slightly differently to the pressure of being fretted. All of this is a compromise, based on the the string set that's used.
The idea of a zero fret is that at separates the dual purposes of the nut into two pieces - string separation and spacing (still done by the nut), and the establishment of the open-string length (by the zero-fret). With a zero-fret, nut wear, or un-careful nut-filing, doesn't throw off the intonation. (With a regular nut, if you file it improperly, you can throw off the actual point of contact of the string in the nut-slot.) The down-side of a zero-fret is that you can't really adjust the string height at the nut-end, at least not separately for the different strings. And of course you can wear little grooves in the zero-fret, over time, just like nut slots can be worn down.
Locking nuts help preserve tune with trem-equipped guitars. PRS takes the different approach of trying to minimize friction at the nut, and having locking tuners. And the PRS headstock is designed so that all of the strings are fairly close to a straight pull over the nut, also to avoid friction and binding.