Why? Company breakups are about increasing competition. It's not about killing the Baby Bells by cutting them off overnight from what they need to survive. ChromeCorp would be both free to cut similar deals with other ad networks, and incentivized to do so, that would be sufficient for governments concerned about monopolies and anti-trust.
It's important to keep things mentally separate here. There is nothing anti-competitive about remote attestation, no more than there is about TLS. It's just far too general a tool for that. Even much more restricted versions as used by the smartphones, games consoles, Windows managed network security etc have never been claimed to be anti-competitive. That would be a very novel legal theory that's unlikely to work on its own (you can use the tech in ways that are anti-competitive, but it needs someone to actually do so).
So if Google were to be broken up, it'd have to be for wider competition and market health concerns, it wouldn't be to do with any specific API getting added to Chrome. And then if they were split up, they'd need to formalize arrangements in contracts that are today informal, like how Chrome is funded exactly. At that point, do you think the newly born AdCorp will just accept paying lots of money for ad impressions to Chrome when the users aren't going to see them? Google tolerates it today for a mixture of reasons e.g. a lot of their own staff use ad blockers, they want to be able to recruit very widely for many different projects, etc. A company specialized only in advertising would have fewer such concerns and could easily demand more aggressive measures, indeed, their new shareholders might insist upon it. Whereas today Google isn't really susceptible to stockholder pressure and is willing to let a lot slide.