You are right in everything, except for one point: regenerative healing jutsu for azure fang if used together with experimental ninjutsu owns a 2 round cd and can be used in round 1, but you are right, none selects it, if able to use it that outclasses hokage tsunade for 1vs1 lineups on the full healing only side.

The main issue of azure fang currently is that her only team support ability on the offensive side is poison tai and is too easily negated by other mains, because it's almost impossible to make use of water enhancement with good outcomes for the simple reason that the water p2w ninjas suks if put together with her on the damage dealing side. The second issue of azure fang is the fact that alone she is too easy to be made unable to do anything.

EDIT: Another thing that makes me feel really sad about her is the fact she owns so nice skills for the damage dealing side, but the current ninja pool makes them wholly useless. I would really love to be able to use her as a nuker, something she could easily be if you give me two water ninjas that boost her and that somehow make her immune, wtf, give us a version of suigetsu, tenten or kabuto that make her able to land damage as much freely as root of warrior does for mbs or 4th mystery of sb does for fire ninjas, and not only to be used as a 'support'.