It goes both sides though, sometimes damage is what allows you to clear some content (maybe excluding Joan with her spear, but even that may not be enough).
And I deemed Herc the best choice for team of Awakened Tit/Hastur/SR Cybele/Ithaqua, before I had Shingen and before Herc's axe was even added. Could other Soul do job ? Absolutely, but I still think she was best choice here for fat Full Break damage and enough speed to keeping up with rest of team (Axe obviously is really helpful here).
Don't get me wrong here, I just want to state, that even without her axe Herc has some uses and is not necessarily worse than some other Soul.
It's not only about 'missing' Kamihime. You can have some debuffer Kamihime and you may want Axe because it'll let you replace her with someone else. Such is the case with mentioned before dark team. Dejnov has Susanoo, Osiris and debuffer SRs (Lu Bu, Nyar). If you'll get Thanatos and go for all-hime DEF down, you'll have to throw either Susanoo (most probably) or Osiris.
Tbh in this situation I'd either go with Mordred/Thanatos/Susanoo/Nyar/Osiris for balanced team, or Herc (with at least 1LB axe)/Thanatos/Susanoo/Lu Bu/Osiris for offensive (for some BT raid kicking or when team is ready to set Mordred aside).