All the mess could be avoided by actually tackling the real problem: The banner. Making it decent is actually the only possible a solution; all else, including this request, although welcome and helpful, is but a clumsy work-around.
Still, the staff refused to make it less of an annoyance and gave no serious justification for it, the real one being that Stack wants to make money by tracking visitors. A small banner is ignored — that's what they learned from the previous version of the banner, which was an unobtrusive footer. This new banner occludes content, thus users have no choice but to dismiss it to move on.
To add up, there is no "reject all" button (proposal), a nice strategy to induce users to give "consent".
The new cookies banner has been launched several months ago. Many bugs have been filed since, as well as several complaints on its intrusiveness. One would expect Stack Exchange to value enough its community to at least have sorted out this obvious request beforehand. But nah.
A reliable work-around for now is to use an ad-blocker. For example, these Ublock directives clean up much of the rubbish in the user interface, respectively the banner, the big "sign up to join this community" header, and the Teams advertisement:
askubuntu.com##.js-consent-banner
mathoverflow.net##.js-consent-banner
serverfault.com##.js-consent-banner
stackexchange.com##.js-consent-banner
stackoverflow.com##.js-consent-banner
superuser.com##.js-consent-banner
askubuntu.com##.js-dismissable-hero
mathoverflow.net##.js-dismissable-hero
serverfault.com##.js-dismissable-hero
stackexchange.com##.js-dismissable-hero
stackoverflow.com##.js-dismissable-hero
superuser.com##.js-dismissable-hero
askubuntu.com##.ps-relative.js-freemium-cta
mathoverflow.net##.ps-relative.js-freemium-cta
serverfault.com##.ps-relative.js-freemium-cta
stackexchange.com##.ps-relative.js-freemium-cta
stackoverflow.com##.ps-relative.js-freemium-cta
superuser.com##.ps-relative.js-freemium-cta