The point of killing third party cookies is to prevent a tracking identifier cookie that uniquely identifies your browser from being reused across different sites.

So you can of course host your own scripts and run them on your own origin, lets call it site1.com. But when your site1.com includes a third party iframe to e.g. googleanalytics.com, and that frame sets a cookie on itself, the cookie is now silently dropped. Then when site2.com later includes the googleanalytics.com frame, the frame cannot immediately link the two browsers. There are other ways to “link” browsers across origins, like browser fingerprinting or in many cases just IP, but they are not usually guaranteed to be 100% reliable.

Blocking third party cookies is standard obvious privacy functionality, but google has held out because it affects their bottom line. So IIUIC they had to wait until they implemented something that protects their bottom line (the chrome-only “privacy sandbox”).