I don't see why such an app is required. If user need to search for something, they can use their browser. And if someone wants to have a browser app/widget they can download it from the Play store.
This "solution" by Google is just a way to prevent more fines, while most people will still have a huge Google search bar on their phone and Google can make some extra money.
You've just shifted the problem down the stack.
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.