Yeah, moving from FPTP to Approval voting or Cordocet voting or something would be a huge improvement, at least in those terms. It's a tough fight though. Critics say "oooh, that's too complicated, it'll confuse the voters" blah, blah. Hell, in NC the SBOE (State Board of Elections) has used "voter confusion" as justification for policies that historically made it all but impossible for 3rd party candidates to even get on the ballot.
To give some perspective... in NC, in the modern era, only one 3rd party has ever achieved ballot access (the Libertarian Party). And until a few years ago, the rules were rigged to force the LP to constantly recertify through a long, tedious and expensive petitioning process every election cycle.
When the LP, Green Party and others sued the SBOE, they actually argued that having "too many candidates on the ballot could confuse voters", despite their essentially never being more than 3 candidates for any given office. Further, in most election years many, many races are actually uncontested! But we'll confuse the voters if we allow the Libertarian Party, Green Party, Constitution Party, etc. on the ballot. Sheesh.
I suppose the only problem then is, where would they find one?