"I expanded the context simply because we live in a world where many people think that a number in a book has an equivalant on a webpage, or that the XREF ID (aka person ID) will remain consistant over the life of the record. This creates problems for people and software developers."
Frankly I assume that the value of genealogical numbering systems where they are traditionally used is self-evident and doesn't merit explanation. The original question essentially was would you use Ancestral Lines on FTM Ahnentafel reports if given a choice? Expanding the context by introducing other elements like books and webpages will just confuse the uninitiated.
Anyway, it looks like we're going to have a discussion about the merits of genealogical systems in general. Okay. But please don't forget to answer the original question. :)
I personally believe that this numbering system has major advatages for small studies and that I may consider its use in cases were I'm developing an "ancestry only" tree for someone (i.e. who were my great-great grandparents?) similar to a "FAN CHART".
I can't imagine an Ahnentafel or Register report without numbers. They demonstrate the structure--the relationships of all the people listed. That's why they've been used in such genealogies for hundreds of years. The concept of the Ahnentafel system, in fact, was published in 1590. Something employed for so long obviously has intrinsic value.
This particular numbering system could be used for descendants. It would just be flipped on its head, much like Eytzinger-Sosa's methods were to make the register-style of numbering descendants.
silverfox also mentioned this point about FTM books. I must admit my use of FTM's publishing capabilities is rather limited, and I've never used the book feature. Still, if numbering systems are imposed on books by FTM, well, I think that's silly.