Simplest isn't necessarily the best, and this is probably one of the best examples you could find. FPTP is used in UK too, and UK politics suck as a result, but I'd say that US politics suck so much worse, and to a very large extent it's thanks to FPTP.
All the problems stem from the fact that FPTP encourages people to not 'waste their vote' and vote for a candidate that's more likely to win, rather than the candidate they like the most. This is already a huge problem, this isn't how democracy is meant to work. But that naturally leads to the number of parties being reduced to the smallest viable number, which is two. And once you have a two-party system it brings an avalanche of problems.
In the UK, in spite of having FPTP we're slightly beginning to move away from the two party system largely thanks to how useless both 'main' parties have proven themselves, but in US for various reasons I'm not seeing any likelyhood of a move away from the two-party system, and it's a massive problem.
First, with a two-party system you get the same problem as having a choice between only two competing options when buying a car, or a computer, or anything else. As one of the two main parties you don't have to be actually popular, you just have to be less unpopular than the other main party. I believe you're seeing it abundantly clear now. As I see it several most recent US elections were to a large extent won not by people voting for a candidate but against the other candidate. It's accepted that the winning candidate will suck, but the hope is they won't suck as much as the other guy/woman. Obviously this doesn't lead to great quality of leadership.
But I believe the two-party system in US has lead to a even bigger problem. After so many years of a two-party system a lot of people think about politics in a fundamentally binary way and seem completely incapable of thinking in any other way. These people don't see good and bad policies, they see Democrat and Republican policies. This leads to a whole lot of rationalization and blinkered thinking and people voting for laws and candidates in spite of being obviously bad so long as it's coming from their team.
US desperately needs other parties in the mix. Even if they won't immediately start winning (it will probably take time) the threat of them becoming serious players may force the main parties to push their policies in a more popular direction. As it stands thanks to the fptp system the main parties can safely ignore independents/third parties as irrelevant weirdos and continue to push lobbyist-dictated policies.