That means that until and unless a 3rd party candidate manages to completely overshadow one of the major political parties, which is effectively never going to happen,

It could happen sometimes, although it’s admittedly rare. Maine has an independent senator, Nebraska has an independent senator who’s running a strikingly close race against the Republican. In Alaska a couple of years ago the same thing happened although the independent didn’t win. I think Jesse Ventura was an independent in Minnesota. But they are one-off cases and not a systematically viable across the whole system.