If you want to use product A, you need to also use product B. That alone is sufficient to create an antitrust violation. It's almost literally the textbook example of an antitrust violation.
But Google didn't stop there--they required exclusivity for product B for several years, and even after that ended they still required premium placement. Either way, they just compounded the severity of the antitrust violation.
Product A, i.e., the search engine, is not just profit-making, it's been Google's primary source of revenue for the the past decade. Google makes billions on paid search results placement. It's the foundation of their business model. Display Ads, Android, etc., are relative drops in the bucket in comparison.
So, do we want to subsidize it? No, because it's a private product offered for profit.
Should we let it die? Sure. Google's not the best search engine anymore, just the biggest. If it has to face some competition, they'll start improving the product again, which benefits everyone. And if it doesn't improve the product, it deserves to die.
It might be that I don't see how what you classify as Product A and Product B are different products. I see Product B as the monetization feature of Product A. If I "squint" I can see how they are different products but I am not convinced.
Product A is the search engine, so you're paying for search results placement, which is how Google monetizes search.
Product B is display ads, which are displayed on other (almost always non-Google) websites. No searching involved...
I don't see how they're even remotely the same product. They're similar in the sense that their forms of advertising, but they're very different forms of advertising. Search placement is intentional advertising (in the sense of targeting prospective customer's "intent" to use/buy) while display ads are awareness advertising. The proof is in the very different rates: search engine placement terms can cost several dollars per search. That same amount could buy hundreds or even millions of display impressions.
Product A: dominant search product
Product B: non-dominant advertising product.
If you want to use product A, you need to also use product B. That alone is sufficient to create an antitrust violation. It's almost literally the textbook example of an antitrust violation.
But Google didn't stop there--they required exclusivity for product B for several years, and even after that ended they still required premium placement. Either way, they just compounded the severity of the antitrust violation.