So assuming the company is splits into Google and AdWords, would Google be forced to work with AdWords or are they allowed to use different providers? Are they allowed to create their own competitor to AdWords? Which problem is this solving?

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.

I'll give an example of a Canadian vertically integrated monopoly: BCE (Bell Canada Enterprises). BCE grew out of the incumbent phone company (Bell) in most of Ontario and Quebec. Over the years it has used the massive profits from telecom to extends its reach into other sectors of the economy. Over the past 10-15 years, it has made quite a few acquisition of various content producers. Most notably to me was the purchase of CTV and Discovery Channel.

Back in the 1980s, Ottawa had a local independent broadcast named CJOH. They produced their own local news at 6pm and late night. The CJOH news team was well respected and an active participant in the community. CJOH eventually got purchased by CTV and ultimately landed under the control of BCE / Bell Media. Shortly after Bell Media gained control a few years ago, they laid off longtime anchor Carol Anne Meehan. Not a good move in my view, as they brought on an entirely new and young team. Further cuts to the news staff have happened over the last few years as increasing use of technology has allowed further staff cuts -- everyone from camerapeople to editors and technical support staff. Each cut means one less means by which the news organization can learn about things that are happening in our community.

The acquisition of Discovery Channel was even worse in my opinion. From 1995 to 2018 Discovery Channel ran a show called Daily Planet, which was one of the only daily science news shows. This was a wonderful way to find out about all kinds of cool things going on in the world of science and technology. It aired on weekdays at 7pm after the 6 o'clock news. Bell Media cancelled the show on May 23, 2018.

The loss of Daily Planet is, in my opion, worse than that of a local news channel. Daily Planet was part of the reason for the existence of Discovery Channel. There are no real replacements being broadcast that I know of.

The reason I bring all this up is to show how the priorities of a monopoly impact existing services that are a public benefit. In my opinion, the BCE layoffs were not the result of the company losing money. The reasons were to free up cash flow to pay for Bell Canada's massive investments in building out its Fibre To The Home network. Bell has spent billions of dollars thus far building out FTTH across Ontario and Quebec, acquired the incumbent in Manitoba. Purchasing content producers that were once separate entities, then gutting them and using the savings to pay for FTTH construction is a brilliant strategy. Money that was previously an expense gets turned into capex that builds a new asset.

Sadly, our phone and TV bills don't go down in price despite us getting less new content. I had the chance to speak to folks at Discovery Channel at a conference back in the 1990s when I was a teenager, and their enthusiasm about bringing real science content to the public was amazing. I'm sad this has been lost at the alter of corporate greed.

It's impossible to remove that conflict of interest. The search engine maximizes expected utility when serving ads: argmax(predicted-click-through-rate * cost-per-click). That's the only rational thing to ask for from an advertising network, and it's what the advertiser optimizes for as well by running the ad auction in the first place. It doesn't matter who computes the ad-quality score (the predictor of click-through rate); rational actors with sufficient information will agree on the value.

One could artificially prevent the search engine from e.g. sending keywords and viewer profiles to the ad network, but that is a completely separate regulatory approach from monopoly-busting.

While we're stumbling around the regulatory possibility landscape why not just ban advertising altogether? It's a ~1% drain on the economy that people who know better go out of their way to block.

Ad networks were separate years ago! Strangely enough they were acquired. Google bought AdSense and Sprinks in 2003, dMark Broadcasting in 2006, AdScape and DoubleClick in 2007, AdMob in 2009, Invite Media in 2010, mDialog in 2014, Red Hot Labs in 2015... I'm sure there are more.

I think there might be psychological issues at play here, sadly. If you click onto a news website from a search engine, and it ends up being for the wrong thing, people feel cheated and will want their money back.

This is probably silly, because if you're paying a couple cents per view, you should be concentrating on the value you receive in the aggregate... but people aren't rational, and personally, I don't think I'd be immune to feeling a sense of regret when I spent money on the wrong link.

I'm not going to remember the episode, but I'm pretty sure Planet Money said this is what happened when micropayments were tried in the 90s.

I subscribe to Scroll.com, and I think they've probably got a better model down. Make agreements with lots of sites from different companies, and then offer a bulk subscription which removes ads from all of them. It doesn't let you through paywalls, mind you, but you could imagine a variation on the concept which did.