Breaking them up doesn't mean that Google Search may not monetize by placing AdSense ads, it means that the Corporate structure exists such that Facebook could offer monetization to Google Search at a competing price.
Duck Duck Go isn't a search engine - they don't index the web except in the most misleading sense of the term. It aggregates results from real search engines like Bing and Yandex, who cover the cost of indexing the web with their own version of adsense.
People say google is a filter bubble, but I've forced myself for years to use DDG on most of my machines and it's not a filter bubble. DDG is just terrible at finding useful results even for basic things. Especially searching for programming related things it seems to prefer sites or posts that are a few years old. 95% of my searches retreat to using !g pretty quick. I don't know why I keep adding the extra step. It's like I'm pitching a penny of idealism into a bottomless well hoping it'll turns into a geyser.
People advocate for DDG not because it's better search but because it's better for you. In the similar way that people advocate using free and open source software and not proprietary.
I get that and that's why I use it. But the 95% !g rate makes it a cargo cult exercise. DDG is our best option, but it's not even close to what it needs to be and that's probably because it's copying the biz model of the big guys but can't do well because of the restrictions that make it attractive as an idol. I suspect that if anything ever delivers on an open promise of web search it will operate very differently and may not show up in the next 5-10 years.
Except DDG is a for-profit company that is not open source - one which doesn't submit to third party audits or validate their privacy claims. As a small company, they don't have much to lose either if they did sell your data since they're essentially just a reskin of other search engines.
Breaking them up doesn't mean that Google Search may not monetize by placing AdSense ads, it means that the Corporate structure exists such that Facebook could offer monetization to Google Search at a competing price.
And with disparate boards/shareholders.