I thought this was only about the search app/widget, not also about the browser and the browsers default search engine. My bad.

But I don't think it's just shifting down the problem.

Right now the search app, browser and search engine of the browser are all Google. I don't think an unremovable* search widget on phones is necessary. And I think Google wants to keep it there because they know people will choose Google, especially since that one is installed by default and users just get the choice between installing an extra app or skip that step.

*unless you install a new launcher.

The EU had a solution for that when Microsoft was doing the same thing with browsers: post install offer the user a choice of web browsers, which IIRC was based on market share.