I think I disagree: I think it was Reagan and JFK who decided; the correct statement would be that others pushed against Reagan and JFK on their choice.
JFK loathed LBJ; so did the entire Kennedy family and most of his entourage.
And no matter what you may have read lately, Reagan was NOT a big fan of G.H.W. Bush.
I lived through those times, my memory is far better than most, and my info isn't solely from any form of the MSM nor memoirs.