Why organizing elements in increasing mass numbers would be rejected as a form of the periodic table?

Answer is: because one element has more isotopes (differente numbers of neutrons), that means differente mass number. Atomic number is unique and defines an element.

Atomic number (Z) is total number of protons and mass number (A) is total number of protons and neutrons in a nucleus.

Atomic number is the number of protons.

Atomic mass on the other hand is the number of protons, neutrons and electrons. The percentages of isotopes of an elemnt my be considered changed form one publication to another. So as a result d ifferent periodic tables give differing atomic masses. This is the reason why organizing elements in increasing mass numbers would be rejected as a form of the periodic table.