That makes a strange legal argument, though. You can't say that Apple putting the default up for bid is anti-competitive behavior by Google. So would you say that Google can't bid in the auction because that in itself is anti-competitive? That also seems like a tough legal argument to make (though I am not an expert on this) because it means that basically everybody is allowed to be in the auction except for Google.

You could definitely say it was anti-competitive if Google was paying more than they earned from this search traffic. But I seriously doubt they are doing that.

They aren’t specifically trying to kill other search engines though. They’re just trying to acquire more users, by being the default service.

Apple made them the default because they are the best at monetization of large volumes of search queries from iOS devices. If another company was better at it, they'd put in a higher bid and rake in the profits.