It quite true that initiative is not the sole deciding factor in a fight, but it is considered the most important single stat in the game do to just the sheer amount that it can affect in battle, or to put simply 99% of the time you want to have the higher initiative. Even the team above can benefit from having the initiative advantage, for heal team getting off a heal before a jinpachi or madara ignites your lineup can be the difference maker, with masked man mean whether or not going for a same position interrupt is viable in a prompt mystery battle, and kushina can benefit by going into round 2 with a suppressing immunity that can easily be comboed into immobile.

Very true, though barrier ninja are still highly valued for many parts of the game at this point. I would say having the total initiative advantage is not as huge now for some teams, though good initiative is really useful, even more so for interrupter ninja like shark Kisame, which if po1 and faster can stop your opponent from getting any mystery that turn. Its definitely a stat that one should't be ignoring if their trying to do well in pvp that's for sure.