Only a few elements could be arranged into triads. As the concept did not work for the rest of the elements it could not form basis of classification of elements.
Also, 3 elements per group is a very small number to divide the elements. This would divide the known elements into about 40 groups.
The idea of classification is to present the elements in an easy, simple and organized manner and division into a large number of groups would not achieve this.
Such a classification would be difficult to put up in a tabular form.