Google the search engine could charge an ad network a lot for the right to show sponsored results and provide analytics.
Android/Chrome could charge a lot for user data, analytics, have their own mobile ad network and app store. Android could also start charging a licensing fee to vendors
Etc etc
It seems like it just creates a lot of inefficiency.
It was always a mixture of both scenarios.
Yahoo prior to using AltaVista, Inktomi or Google had its own search tech - going back to 1995 - and its own advertising network.
AltaVista had its own search tech and its own ad network.
Lycos, a top 5 portal at the time, had its own search tech and its own ad network.
GoTo.com, very popular in its day, was both a search engine (acquired) paired up with its own famous ad system.
For several years AOL flirted on & off again with their own search tech, initially based on WebCrawler, prior to and after their deal with Excite. They also ran their own ad network.
Operating systems might have to get lumped into the 'everything else' bucket if they don't generate enough revenue through charging manufacturers or getting paid by ad networks.
Splitting up these things may not make any of the markets (search, ads, OSes, other consumer services, other enterprise/cloud services) more competitive, but it would prevent using monopoly positions in search and ads to subsidize Google products in other markets.