"To me, having a browser setting for cookies is the only sane way to handle this, it's surprising that this was not considered from the beginning."

This is exactly what browsers did back the 90s, they asked about every single cookie.

Then browsers got configurable options to simply accept either all cookies, no cookies, or only first party cookies (excluding third party sites unrelated to the domain you visited).

For now well over 20 years I have disabled 3rd party cookies in all browsers I use, and only in a few cases overall did I need to make exemptions.