Inheritor is the most powerful option (massive stat boosts, magic system, etc) we have which does not involve eliminating our ability to mitigate our Tyrant's Doom. So I quite like it, from a Hunger/Not Dying OTP perspective. Second, I think the scene when we meet with Erii will be rather heartwarming if we get there, so that's a big plus.
The other benefits are sort of window dressing, really.
It's interesting that Hunger's Soul contains multitudes, however. Inheritor is interestingly thematically appropriate to Hunger given his choice to burn away everything *except* his memories of his companions.
Well.. if it helps decide, Rihaku did say that Inheritor/Unerring is stronger than Stranglesthorn against the vast majority of our enemies.