If some modes of operations of AES are not secure (like ECB or CBC), which are prone to bit flipping / manipulation attacks, and why they haven't they been banned or advised against by NIST for other bodies and are still recommended?
The last publication that I am aware of is: Recommendation for Block Cipher Modes of Operation.
From the document:
"This recommendation specifies five confidentiality modes of operation for symmetric key block cipher algorithms, such as the algorithm specified in FIPS Pub. 197, the Advanced Encryption Standard (AES) . The modes may be used in conjunction with any symmetric key block cipher algorithm that is approved by a Federal Information Processing Standard (FIPS). The five modes—the Electronic Codebook (ECB), Cipher Block Chaining (CBC), Cipher Feedback (CFB), Output Feedback (OFB), and Counter (CTR) modes—can provide data confidentiality."