I once had to wait 3 months for a business visa from India’s San Francisco consulate, which granted sets a standard for incompetence I have never seen surpassed.
Someone who
1. travels internationally multiple times a month, and
2. has a weak passport which rarely gets multiple entry visas
could conceivably require 2 or more passports.
While I have never heard of 3-4 regular passports as OP refers to, nonetheless I can see how some occupations like an airline crew member flying long hauls with a weak passport (especially one issued with 5 year or less validity) would easily need 3 passports.
I expect the frequency of travel and its incompatibility with a K-1 visa will be the topic of discussion at the interview.
As someone who held a green card while living in the U.S., it was significantly more difficult for me to get a visa than it was for U.S. citizens, and when I have looked at the process for my wife before naturalized, I said “nah, easier to get U.S. passport”.