What is the purpose of having a table NOT LOGGED INITIALLY
The classic real-world example is where the table I am creating is a copy from a static external source.  If the DB fails during the initial load, it will be faster to just drop the partially loaded table and start my import operation over from the beginning, than to suffer the overhead of fully logging the transaction.

For example, I am loading my reporting environment with a list of customers from my transactional environment's backup file.