How do I change the default search engine to DuckDuckGo in Safari on a new iPhone?

The phone is new, and the default search engine is Google. I followed the advice I found: Go to Settings>Search>Search Engine, and clicked on DuckDuckGo. I brought up Safari, and still the search engine was Google. I powered down, and powered back up. In Settings>Search>Search Engine, Duck Duck Go was still selected, but when I launched Safari, Google was still the search engine.

[Re-Titled by Moderator]