The answer is that the work by Boenninghausen is a composition of original provings, discussions with Hahnemann and clinical experience.
The symptoms produced without a known causation would give a whole heap of remedies for consideration, Phos being among the top. However, in provings, in clinical experience, the action of potatoes on the economy give rise to a known effect, for which these 5 remedies appear to have an affinity for.
KENT, who took all of his rubrics from other repertories, has this list, of which ALUM features heavily in all of them. He also has other remedies featured in Boenninghausens work. If he had disagreed, he would have removed them.
However, in using the T.P.B. for a number of years, I have found the remedies suggested to be accurate to the extent that if one is STRONGLY suggested, and I cannot find the match in the M.M., I will still try it if all the other symptoms fit.
If Boenninghausen had not suffered a catastrophic loss of all his work in a fire, I am sure we would know why he included these medicines into the T.P.B.