It already does that! 1Blocker lets you specify a list of websites for which cookies won't be sent in the request headers. So I suppose the API indeed supports this feature.
https://developer.apple.com/documentation/safariservices/cre...
https://kb.adguard.com/en/general/how-to-create-your-own-ad-...
(I switched from 1Blocker to Adguard because 1Blocker wasn't working very well for me.)