But the app changes my default search page and new tab home page without my permission. I installed the app to get my duck email address then immediately disabled it.
I'm not sure which "app" you are referring to in this case, but generally private search is a key part of being private online. In every browser but Chrome, you can, however, subsequently change the search engine if you want. It's not our fault you can't do it in Chrome -- that is their restriction.