Client side blocking (by that I mean removing them after the tab/page close)? First for third party cookies, then for all of them, and add a "button" next to the url bar, to enable cookies for that specific site (to allow logins).

This breaks multiple desirable uses of cookies, unless they're explicitly allowed on a per-site basis. It doesn't help if a site uses cookies for both desirable and undesirable purposes. If this solution became ubiquitous, I'd predict websites would start showing popup banners nagging you to click the "enable cookies" button from next to the URL bar. Finally, even if this did work to stop websites from tracking users via cookies, the data harvesters would simply keep using non-cookie tracking methods like browser fingerprinting.

In contrast, the GDPR does not place requirements for cookies if they're not used for storing or processing personal data (the ePrivacy directive which I'm less familiar with might require a notification about them). It does not even require a popup or user's confirmation if personal data is processed on a legal basis other than consent (though these uses may need to be listed in some kind of available privacy policy document). Finally, as GDPR is mostly technology agnostic, its requirements remain the same regardless of whether the data collection is done using cookies or any other means.