That would be a nice commercial for duckduckgo. But it would totally make sense for the user. I bet Google payed a lot of money for that not to happen.
I suspect the objection had to do with some misinformation regarding the Duckduckgo browser. I remember reading about the issue and thinking it was about search, too.
The DDG CEO wrote up a response on Reddit and it explains it very well. Here’s a link to the comment on the Wayback machine.