EG Ecosia is a recent entry, so it does seem that Apple does look into this and introduce new options that can serve their audience size with sufficient quality results. Getting included seems more about making a unique and useful product.

Other than downloading another web browser which features more fine tuning options for web browsing, one can also download safari extensions that increase the search capability in both mobile/desktop safari. One such extension is called xSearch, which presents the familiar idea of using shortcut terms to direct search queries to any number of custom configurable search providers. The share sheet extension also extends this into other apps, and similarly because it uses the standard URL scheme, it can push queries into entirely different apps other than Safari for the search to take place. (eg search this text in the Twitter app.)