Why were the Rabbis so interested in finding out how many letters, words, and verses are in a Sefer Torah? The same question applies to their further questions about how many were in Tehillim and in Chronicles.
Bob Dale, Canada
It seems from the commentaries that the most basic answer to your question is that the Gemara relates these details not to express how interested the Chachamim were in counting the letters, etc., but rather to relate how thorough they were in their learning. They were so well-acquainted with the Torah that they knew even the counts of the letters, words, and verses. It showed their complete mastery of Tanach, and their intimate connection with it.
Another aspect of this incredible knowledge is the many Gematriyos and acronyms that result (some of which are cited by the Maharsha and other commentaries here), with which the Chachamim presumably were thoroughly conversant.
Kol Tuv,
Eliezer Chrysler