The seventy-two answer a demand that runs through the whole of Renaissance and early modern occult philosophy: the demand for a system with no gaps.
Agrippa's Three Books of Occult Philosophy, in 1533, is the monument to it. Its ambition is total correspondence, every number, letter, planet, sign, metal, plant, stone, humour, angel and name placed in relation to every other, so that the whole of creation forms one articulated structure and knowledge of any part gives access to the rest. That programme is what the seventy-two were absorbed into, and it explains what happened to them.
A list of seventy-two names, generated by a fixed procedure, was exactly the kind of object such a system required: complete, non-arbitrary, and divisible. Seventy-two divides the circle into five-degree segments. It divides into nine groups of eight for the choirs and the sephiroth. It matches the count of the demons once the demons had been counted to match. Every one of these divisions is exact, and exactness was taken as confirmation.
The seventy-two therefore accumulated correspondences faster than almost any other element of the system, and they accumulated them for structural rather than doctrinal reasons. Something that divides cleanly gets used.
That appetite has not gone away, and it is worth recognising it in the modern literature as well as the historical. A birth-date system covering every day of the year with no remainder, a table with a column for every category, an angel for every degree, these satisfy the same requirement, that the system should close.
Systems that close are satisfying and are not, on that account, true. The completeness of the seventy-two is a property of the number, and it was available to be found by anyone who divided three hundred and sixty by it.