Google wanted to (that's why they created stuff like FLoC) but other advertisers didn't like that and went to the market authority. They demanded the ability to track users, arguing that the system would give Google an unfair advantage.

After years of back and forth, Google abandoned their efforts. You can still disable third party cookies, in fact I don't think there's been a version of Chrome that doesn't let you block them. Go to your settings and set "third part cookies" to always be blocked. By default, grouped sites may be permitted to read each other's cookies, but you can disable that too.

The problem Google faces is changing the default, simply blocking third party cookie has never been an issue.