Click attribution can be handled completely server side. The browser can't protect you.
If you don't want to be tracked, then don't click on the ads.
If you don't want to be tracked, then don't click on the ads.
You could potentially stop their code from running on your computer, but you can't stop them from running code on their servers, and if you make yourself hard enough to fingerprint, CAPTCHAs become impossibly difficult.
Plain old cookies and unique url parameters are the bread and butter of ad tracking. It is a much more accurate and practical way of tracking you.
It is just that trackers are relying more on first party cookies than 3rd party ones.