Even if the U.S. moved to your preferred method, we would still wind up with two primary parties which perhaps have to form a coalition government with smaller parties who could play kingmaker roles. While as in Canada which two parties they were might change from time to time, it still basically always comes down to which wing can capture more of the centrist vote. It makes precious little difference whether a coalition is formed after an election as typical in places like Europe, Israel, etc. or beforehand as typical in the U.S. via a primary process which determines which wing of a primary party will be dominant and have its preferred candidate run in the general election.
If you or anyone else can show an exa
My method wouldn't decrease the strength of the two party system, but it would allow people to at least vote their conscience first and then vote second based on who you want if your ideal candidate doesn't win.
It is a system that solves many issues that many Americans bitch and complain about:
1. That third parties are nothing but spoilers. Well, have a Single Transferable Vote, and no longer are third parties spoilers, since the voter still has the option for voting for the major party candidate they like.
2. That third parties are never going to be able to break into the current system. Well, allow third parties to be voted for by every single citizen without them being simply a possible spoiler, and you might get Party X and Party Y voters actually voting for a third party candidate as their first choice, altering the election itself, because third parties are no longer simply spoiler parties.
In essence, "my method" isn't just theory, but is in actual use in real life countries around the world.
And again, my answer puts the OPs question to rest.
In a first-past-the-post election system, there will likely be two candidates from two parties, because in any election, the least amount of competition anyone can have is exactly 1 other candidate. When the only thing that matters is having 1 more vote than the second-place candidate (first-past-the-post) then you're going to have two major parties and third party spoiler parties that rarely win elective office. And any function major party is not going to split its own vote by running two candidate from the same party.