Earlier quoted context omitted.
Part of the problem is that people are capable of getting to "FPTP is kinda bad", and they have heard enough about experiments with instant-runoff and scoring (incl. approval) methods, where some election had a weird result, that they realize a single-winner system won't fix things, but everyone's conclusion is: "some kind of proportional system" You can't implement a real government with a metasyntactic electoral sy…
Interesting link, but don't you think it's a bit complicated? I think the opacity of the determination method could lead to a lot of mistrust from the general public. What's the problem with just assigning a number 0-10 for every candidate that you care to, and summing up the points? Or just instant runoff?
That's Range Voting, and it's my preference, but the main problem is that it's complicated both for the voters, and in implementation. Approval Voting is a simplified form (reducing the range to just 0 or 1 vote per candidate) that has many of the same advantages, but has the benefit that people understand it more easily.