The primaries are just a smoke screen. You want to get rid of all the shitty parts of the US voting system? Get rid of the Electoral College. Get rid of the First-Past-the-Post voting system we have been shackled to and all the issues disappear.
CGP Gray did a great series of videos in YouTube like a decade ago about our voting system, alternatives, and how many issues are created from just the Electoral College alone. Unfortunately, those elected stand to lose the most if the process changed so it never will.