Is the use of a 4-round Blake2b permutation in OPP justified? The  MEM-AEAD construction uses a 4-round Blake2b permutation in masked Even-Mansour mode as a (tweakable) block cipher.

4 rounds of the Blake2b permutation are already broken to my knowledge.  Why are the designers justified in their choice?
4 rounds of Blake2b is essentially equivalent to 8 rounds of ChaCha in terms of complexity (a Blake2 round is close to a ChaCha double-round), and that has not yet been broken. Like Richie Frame wrote in a comment, NORX also claims to get away with 4 Blake2 rounds.

One reason ciphers get away with less is that in hash functions all inputs are known and (except for constants) under the attacker's control. In ciphers the key is secret and, unless you take into account related-key attacks and such, not under the attacker's control.