When thinking about about a compensated nut, it can help to first gain a more broad understanding of compensation, as in, what is the purpose?
If all of the strings on the steel string guitar were the same diameter and of identical tension, you would not require any compensation - your saddle would be straight across, perpendicular to the string path. But all the strings are not the same diamter, nor are they of the same tension. So the saddle is angled back on the bass side to "compensate" for the varying string diameters and tensions. The compensated saddle makes the most significant, pragmatic and easiest to maintain change in the otherwise mathematical theory that is the fretted guitar.
Making the mechanical change to the angle of the saddle also affects intonation, or how accurately the notes play up and down the fretboard. Intonation is a precise relationship between nut position, fret position, saddle position and string (or “scale”) length. Improving or perfecting intonation may be the quintessential slippery slope: it is possible to create or modify an acoustic guitar such that it plays so accurately that you will never be invited to play with others. Seriously. Your guitar will sound consistently “out of tune” to them and/or they will always be flat or sharp to you. But it *is* perfectly in pitch. Their instruments are not. Getting an instrument to play that precisely is achievable, though it requires more than just a compensated saddle.
The second change you can make in that direction (with the angled saddle being the first change) is to widen the saddle and individually compensate each string. Not doing so is not wrong. Many prefer the “the happy medium” approach, where the saddle is compensated (pitched at an angle) but remains super thin - a simple, straight line for the strings to pass over.
A compensated nut is a more complex issue, and is the third change you can make. The compensated nut addresses scale length (the precise distance between the nut and the saddle or, more accurately, between the point the string leaves the nut and crests the saddle. Altering scale length is what we did when we compensated the saddle by routing the slot at an angle. Intonation shows its ugly head by reminding us of the precise placement (position) of the frets. Compensating the nut accommodates the relationship between the scale length, the saddle location, and the existing fret placement. Adding a compensated nut (typically) requires an adjustment to the saddle.
But that brings us to our final change that can be made in pursuit of the ultimately accurate fretted instrument: the multi-scale fretboard. The most popular approach to a multi-scale fretboard is perhaps better known as “fanned frets.” Each string is assigned its own scale length and, as a result, each string gets its respective corresponding fret placement (the distance between the frets is exponentially larger for longer scale lengths).