At that point we might as well just skip the entire election process to save money and let the parties work out a power sharing agreement where it alternates every so many years.
Just the opposite, the top two candidates, regardless of what party they're from will appear on the ballot, this would allow people to vote for a 3rd party candidate in the primary without worrying about "wasting" their vote. If the 3rd party candidate is one of the top two they'll appear in the general, if not that voter can still pick the lesser of two evils in the general.
There is no way such a system would ever be allowed to produce a ballot without a Republican and Democrat on it. If you're not on the ballot, you don't get elected. Full stop. There would be all sorts of bizarre measures and "tests" added to such a system before it was ever in place to make sure that only the existing parties would ever be on the ballot.
If anything, I would expect this model to reduce duopoly. An unpopular republican might be overtaken by a candidate from the libertarians in the first round, giving them a shot at victory which they could hardly get if the ghost of "wasted votes" on third-parties was haunting them.