Why was Mendeleev's inclusion of GAPS between known elements in his original Periodic Table rational and shrewd?
Because it allowed him to incorporate NEW discoveries into his Periodic Table.
Mendeleev was shrewd enough to realize that not all the elements were known at the time of his publication of his version the Periodic Table. His Table anticipated the discovery of new elements with properties and chemistry that were similar to the properties and chemistry of already characterized elements in the group.
The discovery of these new elements, and the successful prediction of their chemical and physical properties were convincing support for the utility of the Periodic Table, and the utility of classifying elements by mass. Later discoveries confirmed this utility, and explained the apparent order of the Periodic Table.