The US isn't designed to ensure a two party system. FPTP can allow many parties. The UK is an example of that.
America has two parties because both parties are very internally open. Democrats have given up on that in the last few primaries but that's still very new, and Republicans are still open. You can enter as an outsider and take over the parties. That's how the Republicans ended up with Trump.
If the two parties were less internally democratic you'd see the same situation in the UK where there are two dominant parties and a bunch of smaller parties that occasionally end up in coalition but mostly act to push the main parties around by threatening to take too many votes.
The UK has two major parties, the Tories and Labour. Nobody else has come anywhere near a majority for decades. All of the other parties exist in orbit around one or the other.
The Tories were in a coalition not long ago and if an election were held tomorrow Reform would win a landslide victory. The SNP has dominated Scotland for years.
I'll admit I was being somewhat simplistic blaming exclusively first past the post voting. The real problem is the combination of FPTP and our presidential system. That is what makes the US converge to a two party system, not the open primaries you mention.
The UK having a parliamentary system counteracts this due to when the coalition building step happens. In a parliamentary system, the government is formed via coalition building in the parliament after an election. However, the US being a presidential system means that post-election coalition building would be too late to impact the chief executive, the coalition must be built before the election. This combined with FPTP is what yields our two party system.
For example, imagine the US has an even 50/50 split between Democrats and Republicans. Now imagine the tension in the Democratic Party boils over and the party splits into Liberals and Progressives. Maybe some Republicans were really centrists, so they peel off to the center-left Liberal party. That might leave us with a breakdown of 45% Republicans, 35% Liberals, and 20% Progressives. This almost guarantees the president will be a Republican. Despite attracting a majority of voters, the Progressives and Liberals costs themselves a chance at winning by splitting. They would have a natural incentive to merge their parties again before the next presidential election. But if this was a parliamentary system, the Liberals and Progressives would now make up 55% of the parliament and they could successfully form a government together and choose a PM without having to actually merge parties.
The reason I blamed this entirely on FPTP in my original comment is because something like ranked choice voting is a much more reasonable change that the US could adopt. Shifting from a presidential system to a parliamentary system is an unlikely enough change that I didn't think it was worth mentioning.
America has two parties because both parties are very internally open. Democrats have given up on that in the last few primaries but that's still very new, and Republicans are still open. You can enter as an outsider and take over the parties. That's how the Republicans ended up with Trump.
If the two parties were less internally democratic you'd see the same situation in the UK where there are two dominant parties and a bunch of smaller parties that occasionally end up in coalition but mostly act to push the main parties around by threatening to take too many votes.