There’s quite a few southern states that use runoff voting. Their state legislatures are just as filled with the big two parties as everywhere else. Additionally, the US is not alone in favoring FPTP voting, but many of those other countries still have third parties that are viable in individual regions (Canada and UK, for example). The US is unique in how the big two parties are dominant everywhere at every level.
People focus a lot on FPTP, but it’s not the only factor at work.