What are the benefits of using AEAD algorithms as MAC
Think about 2 special cases when using AEAD:

Some confidential data but blank associated data
Some associated data, but blank confidential data

In first case what you get when using AEAD cipher (e.g. AES-GCM) is just Authenticated Encryption, as there is no associated data.
In second case what you get when using AEAD cipher (again, e.g. AES-GCM) is essentially a MAC - there was nothing to encrypt, and what you actually did was calculation of authentication tag over associated data.
BTW, &quot;What are the benefits of using AEAD algorithms as MAC&quot; and &quot;What is (or was) NIST thinking when they acknowledge(d) using AEAD as MAC?&quot; are actually two different questions. I hope I answered the latter.
EDIT:
If you look at MAC algorithms like Poly1305, Poly1305-AES or CBC-MAC, they also use nonce/iv.