Thanks for the response.

I think we're talking about a few different things. My grumpiness about the meme is that it equates the rule of cool with good GMing. GMs do a lot of stuff to try and make their games more fun - I listed a few of them above. The rule of cool has its place, but using it doesn't make a GM good or a game fun.

Now, I think we're talking about different things for the rule of cool:

Best example I can think of is of a friend playing a game where the party was descending down a long pipe. It was low enough that you couldn’t stand up tall but tall enough that you had to crouch only to an extent. Most people slid down on their ass. My friend asked if he could slide down on his shield and the DM said no. There was no reason for saying no other than to stick to an incredibly strict set of rules that were pre-built.

From what you described, I disagree with the DM's call. D&D's rules don't disallow sliding down pipes on shields. Shield sliding is allowed by the rules. We play TTRPGs for this kind of wackiness. What I consider the rule of cool doesn't come into play here, since there are no rules bent or broken. From what you said, it just seems to be an unfun restrictive call.

When I think of the rule of cool, I'm thinking of allowing actions that significantly depart from the rules of game, balanced against how significantly it changes an outcome. Sliding down a pipe on a shield is not that - shield sliding is totally within the rules, and yes, it should lead to the complications you describe because that's where the fun is. I haven't read the DM manual in a while, but I think it's the first place that I read PC actions should generally be allowed and they should trigger consequences.

So yeah, if I were you, I'd be annoyed with the DM, because they disallowed an action that is totally allowed by the rules. In my mind, rule of cool doesn't come into it.

Totally reasonable rule of cool actions would be stuff like

• a player saying they want to use more than the allowed number of actions per turn to kill the BBEG. If the enemy is basically dead anyway, or combat has turned into a slog (and the PCs are winning), then it doesn't really change the outcome, so the PC should totally be allowed to do it. I'd be less likely to say yes at the start of combat with a BBEG unless the player has a mechanical reason (which means it isn't rule of cool, it's a well prepared PC).
• a player changing an NPC's mind about an issue by doing something awesome or ridiculous. A barbarian can convince a hostile lordling/ladying to sleep with them by using a feat of strength? Sure, that bends how D&D5e suggests aggression/friendliness works, but if it doesn't alter the plot, go for it. If it would make a story arc less fun, then no.

IMO unreasonable rule of cool actions change outcomes for the worse. Stuff like a player wants a one-off at the start of a fight where they use more than the allotted number of actions, and one-shot the BBEG - the same situation above, but with a significant consequence of preventing a dramatic fight. I'd say that changes the rules that the players (including the DM) have agreed upon when they started playing, and it doesn't add any fun. I'd be happy to homebrew a similar effect with balanced consequences out of that moment in the game, but that kind of one off is a bad use of the rule of cool.