There are also trust issues the other way. I've seen a lot of contention between developers and security teams and marketing about putting third party code or proxying third party domains on the first party site for analytics, tracking, ad attribution, etc.
There's all kinds of cryptography available for solving trust problems. I guarantee you that within six months of third party cookies being removed someone will have built an impression signing system that is satisfactory to both the ad companies and the server owners.
I doubt that. Their script could as well be "fetch that script from that URL and run it". They would have fraud detections already in place on their side regardless of which script runs on the client.
but this request could be faked, if the first party wanted to fake the traffic (for example, to make ad revenue). This third party cookie is what prevents this faking at this moment.