I'm not sure what exactly Doubleclick network is, but my proposal is - Google keeps Search + all Ads related stuff, including whatever doubleclick is.
What Google loses is everything client (user) side: Chrome, Android, Gmail and other personal cloud services. Lets call it Foogle :)
Foogle can charge Samsung et al. for its Android and personal cloud services it is running. And use it in its own Pixel devices too. And may elect to make it hard for Google to sniff it, like droppung doobleclick cookies in Foogle Chrome, provide "Foogle Private Relay", et cetera.
You are proposing Chrome+ Everything Else. DOJ doesn't want the Chrome+Search entanglement. So the company getting rid of search would be an alternative idea. Search would still have the adwords revenue model. But it would be separated from the google ad network which is adsense and doubleclick. All your data on Chrome/Android would still be accessible to Doubleclick and Google for personalized ad revenue.
What Google loses is everything client (user) side: Chrome, Android, Gmail and other personal cloud services. Lets call it Foogle :)
Foogle can charge Samsung et al. for its Android and personal cloud services it is running. And use it in its own Pixel devices too. And may elect to make it hard for Google to sniff it, like droppung doobleclick cookies in Foogle Chrome, provide "Foogle Private Relay", et cetera.