Exactly. That's like saying Tesla should be divided into a part making cars, and another part taking payments from buyers.
We could create our own search engine, funded by showing Google Ads, today; the suggestion is that that Ads business be separate to Google's own Search business which happens to use it, but which might easily (except obviously it doesn't) use Facebook Ads or whatever instead.
(I just checked Ask Jeeves and Startpage, and they were both serving ads from Google.)