I'll try to explain why the "old science" is no longer adequate - it is basically about that people are no longer shooting on film, and with digital the expectations have changed. A 24x36mm D800E sensor can deliver prints which in terms of grain-free resolution is very similar to 4x5" film.
Sharpness has always been subjective. Even in the film days many thought that the typical CoCs were too large, because it was based on the assumption that people did not have very good vision or did not really step close to a fine art print. The traditional film CoCs were 0.1mm for 4x5" and 0.03 for 24x36mm, this corresponds to a resolution of perhaps 4 megapixels or so at the DoF edge (!).
It is very obvious that if you take your D800E 36 megapixel camera and base hyperfocal focusing on a 0.03mm CoC the skyline in the horizon will not be critically sharp when you print big and step close.
To be loud and clear - DoF calculators/tables which uses traditional film CoCs are next to useless in the field if you are into high resolution "full DoF" landscape photography. Instead of continuing to explain why it is so useless, I'll try to explain why my method (which certainly is not unique, many use small CoCs these digital days) is good:
My DoF tables aims at a basic goal - that all pixels in the whole scene should be rendered equally sharp, that is when you nose the (sharpened) large print it should be virtually impossible to distinguish the plane of focus from the edge of the DoF. This leads to much narrower DoFs than traditional, but still very much practical you can fulfill this goal without too much diffraction tradeoff even with 40-60 megapixel systems. It is practical and well-defined, anyone understands what the DoF edge means, it means the edge where one begins to see a difference from PoF at maximum enlargement.
Some use 2x pixel size as CoC but actually I think the CoC = Airy disk is more elegant, resolution independent and therefore future proof. That concept is based on the assumption that the optimal lens aperture is somewhat diffraction limited, which it is for deep DoF landscape photography since you want good corner-to-corner performance. I don't see anything that indicates that this balance between lens and sensor resolution will change in the near term.
When aperture is reduced farther the diffraction increases and the CoC should increase too since the edge where one starts to see a difference moves. The actual edge if studied critically is probably somewhere around 0.8 of the Airy disk diameter, but I think that is hair splitting.
Another way to describe the same thing is that the DoF is balanced so that there is no further sharpness gain at the edge if you reduce the CoC. This is a very important property - the CoC is perfectly balanced to achieve peak performance for the DoF you need. You don't stop down more than you need to get everything equally sharp, and the CoC is small enough to avoid the nasty surprise that what you thought should be pixel-sharp really is not.
We assume here that the photographer is aware of how much diffraction affects her/his system, and I do think that is true for most landscape photographers with some experience. The photographer makes a subjective decision of how much f/22 hurts for example to gain DoF, and then it makes perfectly sense that the CoC should follow and match that. One could make all sorts of subjective fine-tunings like having 0.8xAiry disk for larger apertures and 1.5xAiry disk for f/22 since one have already lowered the expectation then, and everyone is free to do that. I do it by estimation by at very small apertures let some things be a bit outside the DoF if necessary.
Holding tight to the old CoC and viewing models all this risk to end up with a Ken Rockwell-esque "4 megapixels is all you need for any use" type of statement, because that is what the typical result of viewing distance calculations is (which is what the old CoC is based upon). But even with my limited experience of fine art printing and display, and high quality photo book prints, I know that in practical viewing in homes and at galleries you can appriciate much higher resolutions than those traditional models lead to. Far from all people nose the prints or even care about image quality in general, but some do, the photographer herself/himself not the least.
You say I don't understand the viewing distance concept, I understand it very well. The traditional thinking which do lead up to "4 megapixels is all you need" is flawed. Make a normal size print of a flower and then make a large size print of a detailed landscape, perhaps a city at a distance. Hang them on the wall and look how people that look at the prints behave. For the flower they will behave nicely and stand at a distance so they can take in the whole image at once. For the detailed landscape they won't be so nice. They will step up close and inspect those interesting small details (if there's something there to find). 100% pixel peep is quite real to represent what will be visible for this type of print done at 150-200 ppi. For high quality photo books the same things happens but in a smaller format. The viewing condition is very much relative depending on subject, print size and presentation. Detailed landscape scenes printed big presented in a gallery mounted at comfortable viewing height is an example where the prints will face very close inspection indeed.
I have a 33 megapixel system. When I shoot I generally don't know where the picture will end up, but I preferably want to come home with files that can be printed as sharp as possible in large sizes. Otherwise I'd use a much lower cost and lighter hand-held system with less megapixels (which I do for other types of photography). Tables based on the DoF/CoC model described above works and helps me achieve this goal, and I don't think I'm unique in having this goal, but rather I think it is what landscape photographers with high resolution gear generally want -- that is getting the sharpest possible image the gear can provide.
Obviously there are situations when one has a more relaxed relationship to the DoF, for example if we don't hyperfocal or tilt but actually put the focal plane at the main subject and it clearly is the main one then we don't need to worry as much of how sharp the DoF edges are. In any case the traditional CoCs are not delivering what I and many others expect, so we need something other, and I think I have (and the others with similar solutions) have come up with a good way that actually works is easy to understand and gives expected results, and is also a much better basis to use for "relaxed estimations" than CoCs that are heavily relaxed in the first place.
Ok this was long, but I believe very much in this model and I'm using it with good results, and I see others use similar models.
The thing that is always asked is "how to make the image as sharp as possible?". Use a stable tripod, use mirror up (if applicable), cable release, use high quality lenses, use proper focusing technique. My article is about focusing technique. Using old-style CoC for deep DoF is not adequate for that purpose. The question is not "how to make the image as sharp as needed?", which the traditional CoC idea tries to answer (focusing technique will be exactly the same though, only the values in the tables will change).