I feel like the Bastones were assigned to "protect" Hy. Corbitt wrote that Carmen used to complain sometimes about having to work for Hy. Plus, assuming Hy did facilitate the $1 million in cash from Vegas to Chicago in 1985 for Aiuppa indicates that Hy was probably connected with some of the more higher ups.

Likely after Giancana was killed in 1975 (at which point Hy was already in his 60s), Hy was reassigned to upper echelon of the Cicero crew, namely Ferriola and Aiuppa. This would make sense because the Bastones were part of Cicero and middle management.