Forcing Google to divest its advertising business would, I think, result in a situation not much different than we have now. Google Search Inc. would get a large payment from Google Ads Inc. to include the latter's ads in the former's search results. Meanwhile Google Search Inc. would have exactly the same incentive it does now to do these kinds of access deals with gatekeepers like Apple and Mozilla. Google Search Inc. would still be using its market power to gain preferred access to customers. In effect you've just added another link in the chain of mutually-beneficial business relationships that locks in a given outcome.
If you also forced Google Search to accept ads from other ad platforms, and other ad platforms thrive, the net effect would be to drain all the value out of the ad networks (of which Google Ads is one). The value in a business process tends to concentrate where the market power is least fragmented, which would be Google Search. Again, it doesn't seem to solve any problem.
The only thing I can think of to remedy the concern here is to ban these types of preferred-access agreements. The problem THEN is that Apple would have a strong incentive to create its own search engine to use in its products, and recapture some of the $8B-12B Google annual payment it would lose (i.e., what Microsoft tried to do with Bing, but never really worked because neither Windows Mobile nor Internet Explorer had a strong market position). This outcome might have positive impacts for customers (more options for search), but it would result in more vertical integration at Apple. It wouldn't really improve the competitive landscape for the DuckDuckGos of the world.
I would be more concerned by anti-competitive issues if 100% of web searches came through these types of preferred-access agreements. As it is, a large fraction of Google searches are made via google.com on a regular web browser, and if a better rival came along, it's easy for customers to switch. This is how Google overtook Altavista. The REAL problem is that it's really hard to build a better mousetrap than Google: It's a service that is inherently expensive to build. It may be one of those situations that economists call a "natural monopoly".