How is it a terrible rule?
I just dislike it. It doesn't reward your cumulative efforts over the group stages like goal difference does. I don't feel sympathy for us in 2006 or South Africa now, though. They've been set against inferior teams and have failed because of their own underperformance, disorganisation, and infighting.
To be honest, I think the head-to-head rule makes a lot of sense in these kind of group stages with wildly uneven opposition, where qualification shouldn't hinge on who put more past Liechtestein or Andorra.
Indeed. Just look at the general logic on going by goal difference. One team could get knocked out by goal difference to another, despite beating that team once or twice. Just based on that it doesn't make sense to do it otherwise. It has helped the US though, when they got through in the Confederations Cup despite losing to Italy.