we will show that every group admitting an unbounded quasi-cocycle into a mixing non-amenable representation is not inner amenable. we will discuss how our approach generalizes a recent result of dahmani, guirardel, and osin on the non-inner amenability of so-called acylindrically hyperbolic groups. other applications such as to central sequences in group-measure space algebras as well as some open problems will also be touched upon. this is based on joint work with ionut chifan and bogdan udrea.