I am not a "Rule of Cool" guy - though I do agree with
@Cordwainer Fish's characterization of an approach to trying things - however, I do think it is either disingenuous or misguided to say that "the rule of cool" is simply about negotiating how to proceed with something and not about the coolness factor. (I mean, "cool" is in the name!).
Yes, the characterization of "whatever seems cool always works and you always win" is also way off base - but in my experience of RoC, the purported "coolness" has been the primary factor in determining if the character can accomplish X thing, either at all or determining the difficulty.
The example I frequently see used is the cliche chandelier swinging. For some people, the mere presence of a chandelier means they want to swing on it and get some bonus for doing so because it is cool (I have seen many people say variations of this on ENWorld in the last 5 years alone, leaving aside the decade I was a regular on the boards in the early 2000s).
For me and my games, swinging on a chandelier might be useful in some way (circumventing a pit, getting from gallery to gallery in a room without having to climb down to floor level, etc. . ) and it might even look cool, but the coolness and the benefit are not connected. I don't think it is mischaracterizing the Rule of Cool to say that for many of the groups/DMs that use it coolness and benefit are connected (to varying degrees).
I can't speak to how common it is, but it certainly isn't uncommon.
And there is nothing wrong with that style, if that is what they like. It is not for me. But guess what, we don't all have to play in the same games and it definitely isn't "bad for the game" more broadly.
I do think it is an example of a reason why it is a good thing to play with different DMs and groups to test out different styles and variations and find what you like and to what degree you like it.