IMHO, Numbering schemes are only good in static environments such as books and are not very good in a dynamic environment. I say this because, any numbering scheme must have a starting point and therefore in a dynamic environment must be generated "on the fly" since the starting point could change depending on the viewpoint of the individual/reader.
Since, genealogy is an ongoing, ever expanding, process the focused starting point for one person in the tree is different than the next person, so any numbering system that starts at one point using generational information to position a person on the tree has its own problems.
This is not to say the "The Ancestral Lines Pairing System" does not have its value and good points. When I do studies of small family groups that include only a few generations of individuals this scheme can break through the log jam of "who begot who".
It does start to break down as we widen the tree and inspect various offshoots of a family and children of children.
Therefore IMO it has great value in ancestral studies for small "on the fly" or larger static reports, books and documents. But has less value with large family groups with "wide" trees where the study include cousins of cousins. In databases that exceed 100 or 1000 of individuals this system could never be use as a perminant numbering system.
Also this numbering system could never be used in the research environment/portion of our databases where several individuals fit the charactorists of a potential ancestor but where proof has not completely been established. We would be unable to assign a number (a good thing) to a potential ancestor yet we would want to report any potential ancestors in their appropriate location in ancestorial trees. Most standard software programs can't handle this issue anyway so it's not a big deal, but if/when a potential ancestor is proven not an ancestor or where controversy between two individuals being "that ancestor" arise some other scheme is needed.