Earlier quoted context omitted.
On iOS — in contrast to Android — you can actually change the default search provider, yes. (On Android you can't change it at all. And so I'm either stuck with a Google search on the Recents menu, or the "this widget could not be found" message)
If you're talking about within the Chrome app on Android then, unless something changed in Marshmallow, you can totally change the default search provider. Chrome > Menu > Settings > Search Engine allows you to change the default search engine in the browser, but you can't add new ones to their list, so it is a limited set of options available. If you're talking about at the Google Now or Siri then as far as I know t…
It’s at the top since 5.0, can’t be removed, can’t be changed.
If you root and disable the Google App (yes, you now need root for that), then it is replaced with an error message, saying that the Google App could not be found.
There is no way to replace it with a search bar for bing, or remove it.