If a moderate candidate is the one who is acceptable to the largest proportion of the voting public, why shouldn't they win? Approval voting allows voters to v

If a moderate candidate is the one who is acceptable to the largest proportion of the voting public, why shouldn't they win? Approval voting allows voters to vote for 3rd party candidates without "throwing their vote away". That would be a huge improvement over first-past-the-post, as 3rd party candidates would have a decent chance of winning if they can make a compelling case to voters.