Nowhere in the primer do I see an assertion that this "replaces" a water calculator as "not needed" as you suggest.
Right up front the primer discusses mash pH goals, and for a baseline it suggests (in addition to calcium chloride) the addition of sauermalz at 2% of grist weight for a basic batch. Then for really light colored brews it informs to up the sauermalz to 3% of grist weight. So, yes, the water chemistry primer does explicitly instruct as to how to move a light colored beer to within the acceptable mash pH window without the use of a calculator. But then it does state that for best results a pH meter is required to hone in the mash pH to 5.3.
Water calculators are not discussed at all within the primer, so there is no guidance within as to whether or not they are needed. This leads me to believe that the primers methods are intended to be sufficient and calculators are in the end not needed. As if they were a requisite, it seems the primer would have mentioned them.
For British type beers and beyond (I.E., higher SRM) the sauermalz addition is no longer mentioned in the primer.
And recently A.J. seems to be of the opinion that for any reasonable Porter or Stout with roasted malts held to no higher than 10% of grist weight, you will most likely hit the mash pH window of acceptability with no baking soda (or other nominally caustic substance) addition required. Although this is latter part is admittedly not part of the primer.
In the end this does not mean that calculators are bunk, but it does show that they are not really necessary.
From my experience in calculator making, it is quite easy to get a calculator to suggest the need for an acid addition for light colored beers, but the truly hard part is getting it right for the really dark colored beers. Much past history and guidance indicating a need for a whopper load of alkalinity for the really dark brews must be overcome if one is to build a calculator that matches with A.J.'s mash pH measurements and experience, which clearly runs counter to this past advice. In another thread, I showed where currently available mash pH assistant calculators forecast everywhere from zero grams of baking soda to 16.5 grams of baking soda as required for the exact same robust stout recipe to hit 5.4 pH during the mash. The results of this observation initially drove me to modify my own software to increase its call for baking soda, but with my next release, I will go noticeably in the opposite direction in order to move MME more in the direction of A.J. deLange's experience (though not exactly matching, with MME being quasi-empirical, and with doubt still remaining on my part due to the impression that all of past history has burned into my thinking). If you can't trust A.J., who can you trust? Yet as much as I desire to trust him in this regard, I admit that I still have doubt...
Putting it all together in relation to the water primer, it may just be that the place where a calculator that is reliable is most needed is for truly robust stouts and other beers with loads of deep roasted grain or malt added, and particularly if such malts/grains exceed 10%.
But this is precisely where the existing calculators show their greatest weakness in agreement. And the primer itself does not address this class of beers.
EDIT: From memory, the various calculators baking soda addition advice was roughly as follows for the above mentioned very robust stout recipe:
EZ Water said some acid was actually needed.
Brewer's Friend in grist mode said no baking soda or acid was needed.
MpH said about 4.5 grams baking soda was needed.
Mash Made Easy said about 8.4 grams of baking soda was needed.
Bru'n Water said about 13.5 grams of baking soda was needed.
Kaiser Water Calculator said 16 grams of baking soda was needed.
Brewer's Friend in SRM color mode said 16.5 grams of baking soda was needed.**
** I followed Kaiser Water Calculator instructions to determine the percentage of color from roasted malts when using Brewer's Friend in SRM color mode, as Kai collaborated on the building of this 'mode' of Brewer's Friend, yet (as I recall, at least) Brewers Friend fails to match his "roasted color percent" instructions. I'm fairly certain that if I did not apply Kai's instructions here, BF would have advised an even higher gram quantity of baking soda.
Edit again: If I had to venture a pure guess, my initial guess would be that A.J.'s advice for this highly robust stout recipe would likely fall somewhere roughly between that of Brewer's Friend in grist mode and MpH.