Which reads much the same as your first paragraph: you're automatically allowing the "something cool" to succeed.
Then I must not have expressed myself clearly enough, because what I was trying to say was completely unrelated to automatic success. Perhaps an example would be more effective.
Imagine, a player is playing a character who’s an archer, and rather than simply aiming to kill their target, they want to try to aim for the target’s hand, to cause them to drop their weapon. However, D&D 5e doesn’t have general rules for called shots or disarm attempts. There are some specific class features that could allow for something like this, such as the Battlemaster fighter’s Disarming Strike maneuver, but let’s say this player’s character doesn’t have such a feature. By a strict reading of RAW, they can’t do it, and the existence of the Disarming Strike maneuver as a Battlemaster class feature suggests that, as far as the system is concerned, this shouldn’t be something just anyone can do. But, it would be pretty cool, and also well within the bounds of what should be reasonably possible (albeit potentially difficult) in a most fantasy settings. So, a DM might decide to disregard the existing rules, or in this case the lack thereof, and improvise a rule with which to resolve this action. Maybe they make their attack roll with disadvantage, and on a hit, they deal only 1 damage but the target drops their weapon. That’s mechanically distinct from and less effective than the Battlemaster’s disarming strike, and still gives the player a way to attempt what they wanted to do.
That, in my understanding, is what “rule of cool” is. Nothing to do with automatic success, just a willingness to go outside the rules as written to enable the player to attempt something cool. It’s really just a more player-focused reframing of what might in other contexts be referred to as “rule zero.”