The solution isn't simple. The solution is changing the way people vote. In order to change the way people vote you have to change the Constitution. To change the Constitution you need to get those two parties that benefit from the current system to change to another system that won't benefit them.
Beyond that, the reason why Proportional Representation works better is:
1) There's more oversight. More political parties to watch out for the corruption. Democrats don't get much pointing out Republican corruption because the Republicans will then point out Democrat corruption. A "you scratch my back" scenario.
2) It's easier to change political parties.
In the UK in the early 1990s this anti-EU political party called UKIP was founded. UKIP is kind of further right, more right than the Tory Party (equivalent of the Republicans). The UK has FPTP just like the USA.
In Germany in 2013 an anti-EU, further right political party called AfD was founded. Germany has PR.
In 2015 UKIP gained 12.6% of the vote in the UK General Election (pre-Brexit). They gained one seat out of 650 seats.
In 2017 the AfD gained 12.6% of the vote in the German Federal Election.
The difference here is that with PR every party can be viable in a short space of time. In the UK lots of people wanted to vote UKIP, and lots did. But because UKIP needed to win more votes than anyone else in a small space, they couldn't.
In fact they had 3.8 million votes to the Lib Dems 2.4 million votes, and the Lib Dems won 8 seats because they have certain areas where they're a viable party.
With PR if people don't like a certain party's policies, they'll vote someone else, which forces the main parties to make sure their policies are in line with what the people want.
In the US the two main parties tell people what they want. They stand on HUGE platforms and people get to decide which is least worst.
UKIP stood on one issue. People will vote on one issue. You can't do that in the US.
If you look at a list of least corrupt countries, they mostly vote Proportional Representation, except Singapore, which is more or less a democratic dictatorship anyway.
If you want an issue like gun control to be SENSIBLE, then you need political parties that are sensible. You get this with PR, because they know if they're not sensible they could easily lose all their seats at the next election. In the US the Dems or Reps could stand on a platform of mating giant bees with cows and they'd know no third party would stand a chance even then.
