You can disable cookies in browsers so that cookies do not persist after session close. Firefox lets you add a whitelist of sites to allow cookies, too.
If I understand the law correctly, your suggestion is good on practice but could be harmful on the long run.
When I click "I agree" I am not agreeing to cookies but rather to tracking. If the website wants to track me with (say) browser fingerprinting, deleting the cookies will not stop them from tracking me across sessions. Even worse: since I agreed they no longer need to show me a warning, so I may not even notice that I may want to revoke that consent.
If I don't want to be tracked, saying "I do not consent" is the only legally-actionable way. Deleting cookies works now because cookies are still cost-effective, but this won't remain true forever.
