2mm is huge in terms of nut height. 1mm is huge when dealing with nut height.
Your average new guitar can often be found with a nut .005"-.010" (.125-.25mm) above the fret plane, which I consider absurdly high, bordering on unplayable. A height of .0005"-.0015" (.013-.038mm) above the plane of the frets is a reasonable ideal to shoot for. Get up past .003" (.075mm) and lower fret intonation can quickly become a mess. Hit .010" (.25mm), and first position chords can become a bear to hold.
Half a the thickness of a US quarter is still in the range of .030", or .75mm. There are areas where this difference is small, but when dealing with nut height it is absolutely enormous.
To put it in perspective, if your frets were perfectly leveled, and were to capo at the first fret, your string would end up departing at around .0005"-.001" above the plane of the frets. If we're talking about the difference in the range half a quarter (the coin), this would be nearly the equivalent of stacking another fret on top of the one you are capoing on. Huge, enormous difference. Tolerances at the nut need to be tight - nearly as tight as the tolerances between one fret and the next when leveling in my opinion.