ChaCha20 is a stream cipher, and there currently isn't any NIST-approved stream cipher at all. The only options areoption is the block cipherscipher AES, Triple (Triple DES and Skipjack (the latter isare only approved for legacy decryption). Of course those block ciphersAES can be (and almost always areis) used in a NIST-approved mode of operation like GCM which make themmakes it behave like a stream cipherscipher, but the underlying ciphers areit's still a block cipherscipher.
The topic of standardizing a stream cipher especially for resource-constrainted environments has been discussed within the NIST since at least 2011. In the Lightweight Crypto Standardization Process, there was at least one stream cipher (Grain-128AEAD) which made it to the final round, but ultimately, it lost to a block cipher.
So the NIST doesn't reject stream ciphers, nor have they (as far as I'm aware) ever recommended against ChaCha20 in particular. It's just that the algorithm hasn't gone through any NIST standardization process. I'm not even sure if Bernstein ever tried, so the chances of a FIPS approval anytime soon seem slim – regardless of whether or not ChaCha20 is a good cipher.