In 2016, I solved a problem of de la Harpe from 2006: Is there a nondiscrete C*-simple group? However the solution was not fully satisfactory, as the C*-simple groups provided (and their operator algebras) are very close to discrete groups. All previously known examples are of this form. In this article I give yet another construction of nondiscrete C*-simple groups. The statement in the title then follows. This in particular gives the first examples of nonelementary C*-simple groups (in Wesolek's sense).
