It is possible, yes. It just hampers much of what people expect modern websites to do (though it hinders abuse, as well, which is good!).
But even GitHub, who proudly declared they had removed all non-essential cookies https://github.blog/2020-12-17-no-cookie-for-you/ added them back https://github.com/github/site-policy/pull/582/files and now if you click either "Manage cookies" or "Do not share my personal information" at the bottom of the page, you'll see they have the common "Required", "Analytics", "Social Media", "Advertising" categories.
GitHub is owned by Microsoft, the company that's putting ads on your start menu, I'm not sure why people are expecting anything less. Whatever they had in terms of culture before acquisition is not the same afterward, even if it changed gradually.
But even GitHub, who proudly declared they had removed all non-essential cookies https://github.blog/2020-12-17-no-cookie-for-you/ added them back https://github.com/github/site-policy/pull/582/files and now if you click either "Manage cookies" or "Do not share my personal information" at the bottom of the page, you'll see they have the common "Required", "Analytics", "Social Media", "Advertising" categories.
(Bummed that they have the Advertising category.)