In homeopathy the division into 18 stages has become so prevalent that it has even been generalized and adapted into dividing the plant kingdom. But is this justified?

The choice of 18 stages in the periodic table could be that it is more than 2 and 8 giving more differentiation or less than 32 and possible to remember.
On the other side the number 32 has strong traditions as a number of stages both from freemasons as well as Kabbalah.
The prevalence of 2, 8, 18 and 32 are the same and equally important (See illustration)

The number 18 is probably based on the most frequent ways of portraying the periodic table, but there are many other ways that are both in 3D as well as circles etc.

Let us look at nature and not the model.
If we could look at the elements themselves the most obvious would be to classify them according to their outer appearance or more precisely their orbitals.

Within the normal range of elements, excluding the hypothetical there are only four kinds of orbitals. So the most valuable approach to classify the periodic table is to divide it in four groups only!

This is based on the mathematics behind the elements from their four quantum numbers, in particular the l number.

When this number is 0 it creates the one S-orbital with two groups, if the number is 1 it creates the three P-orbitals with two groups each, if it is 2 it creates the five D-orbitals with two groups each and if it is 3 it creates the seven F-orbitals also with two groups each.

Each have two groups because the orbitals are divided in a part on each side of the atom and each of them consists of one electron. So the complete orbital needs to electrons to be filled.

The S-orbital is the only spherical. This is the basic simple 3D shape and contains the basic elements in all biology; Na, Ka, Mg, Ca.
This orbital represents the fundamental qualities you need.
It represents your body or self, your home and security, the mineral kingdom.

It is the point, or fixed spot, a crossing or x as a symbol of here, your village, your life, your identity.
This explains the fundamental importance of these salts in the body and in the homeopathic practice.

P-orbitals have a hourglass shape in 3 directions (x, y and z)
The number 3 is a symbol of exchange, communication and breathing. This is the number of the plant kingdom and main gases, and life chemistry.

D-orbitals have five variation
The number 5 is the number of manifestation, it is the number of the polarity of good and bad, of love and hate and strong feelings.
It it the kingdom of animals and transition-metals.

F-orbitals have 7 variations
Number 7 is the number of perfection, man in creation and completion of a process.

To conclude this short comment on the periodic table; number 18 is not obvious or fundamental to the structure, more than 2, 8, 32 or 50.

The division into four sub-regions reflecting the kingdoms as a fractal is missing in the homeopathic literature.
I think that this primary division carries potential to a better approach that is more consistent with the principle in nature and behind the structure of the periodic table.

In short the most important numerology in the periodic table is the qualities of 1, 3, 5 and 7.