Of course they would have an income source. They would sell space on their pages to Google Ads or any competitors, like most websites or media companies (newspaper, tv).
So they'd split off Google Ads then create another ad platform to sell ads on their properties? Why would anyone use the independent Google Ads?
Ok I see what you're saying. You're right that we cannot really separate google from googe ads for their own products.
But Google Ads also sells ads on websites outside google (via Google Adsense). So it might make sense to separate AdSense from Google.
(They're trying to grow a second revenue generator — GCP — but it's not been the success they've hoped; especially compared to Azure. Microsoft had the B2B relationships already in place, while Google has mostly been a B2C company, so they've been struggling to win clients.)