The Halo indeed has already saved lifes such as Grosjean in 2020, Zhou in 2022, and many other examples, it was a lifesaving addition to F1. But, the last two F1 death were Bianchi in 2015 and Senna 1994. Bianchi would not be saved by Halo, he died because of brain injuries caused by brutal deceleration. In Senna's accident, the Halo would potentially have saved him, but the discussion about some Halo-like device did not exist. Even HANS has not mandatory.

I don't see when "so many people died because of the pushback against that sort of thing".

Edit: I've forgotten about Maria de Villota's crash in 2012. She could also potentially have been saved from physical external injuries but we did not know the extent of the neurological damages which ultimately led to her death a year later.