Relevant Brave (Chromium-based browser) bug discussion on exactly this:
https://github.com/brave/brave-browser/issues/1127
They merged in a (partial?) bug fix in 2019:
https://github.com/brave/brave-ios/pull/883
The underlying problem isn't that Google sites are directly excluded, it is that Local Storage, Database Storage, and Service Workers aren't cleared by that setting, and that Google uses those for persistence.
Is this being evil or was support just not added when those were introduced? I have absolutely no idea. But I agree with fixing the underlying bug in Chromium either way.
In the article you can see chrome deleting Apple's local storage, but not Google's.
Not exactly this: according to that bug-report, it happens to non-Google sites as well, if I'm reading it right.
> Local Storage, Database Storage, and Service Workers aren't cleared by that setting, and that Google uses those for persistence.
I always search with a specific Google.ca domain with cookie and javascript disabled. It worked really well and Google knew zero shit about my search habits on my Gmail account.
If you right click inspect and go to applications you can clear all of the site settings. But the end user UI should support this option.
You could argue that a Service Worker should not be cleared since that is more than likely not personal data exactly.