That is how most of the (American) retail auto market works, though, so it's not a strange idea.

More like car manufacturer and car purchase loan provider (if that were something it were offering in-house).

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.

You can already create your own search engine, and have Google serve the same ads on it as they would for their own search. I don't know what the product is called, or what the requirements for signing up for it are, but it is how a lot (most?) of the smaller search engines monetize.

(I just checked Ask Jeeves and Startpage, and they were both serving ads from Google.)

Yes, that's what I said.

Sorry, your use of "could" instead of "can" made it look like a hypothetical.