> But since they also prefer Gore to Bush they have to approve of Gore or else Bush may win.
Only the Gore voters have to do the same thing, and then Nader wins if he has more support. Because a small percentage of people will vote only for their preferred candidate and risk Bush, which will be proportional to the support that candidate has and thus give Nader the win if he actually has more support.
The thing you're really objecting to is why range voting is better than approval voting. With range voting the Nader supporters can give Nader 10, Gore 9 and Bush 0, the Gore voters swap Gore and Nader and then there is less brinkmanship necessary to get the right outcome. But that's the cost of using the one which is easier to explain. And range voting is more complicated than approval voting, but it's simpler than IRV, so you're really just making the argument for range voting over approval voting.
I feel like the trap you're falling into is to grade approval voting based on whether it does what IRV does.
The problem with IRV is that it tends to do crazy things. So for example, imagine everybody expects that in a runoff between Bush and Nader, Bush wins. But between Bush and Gore, Gore wins. So then people who would vote for Nader can't vote for him because it would give the election to Bush again. But even weirder, Bush voters can vote for Nader in order to give the election to Bush. So IRV doesn't solve the most important problem, because people will still be clamoring for third parties not to run and for people not to vote for them for fear that they'll harm the major party most similar to them.