I've always felt strongly against the Grey Jedi concept even all the way back in 2007 when it was in vogue and I felt alone in my opinion. So it has been a tremendous relief to see that the tide has turned against the trend now. That being said, I do disagree with some of your remarks here about the origins of the concept. I don't think either The Force Unleashed or Star Wars: Knights of the Old Republic are to blame. TFU's entire premise is to be a power fantasy, but it doesn't actively try to promote the Grey Jedi concept. At most, it incidentally does through its gameplay and narrative design. KotOR makes a binary distinction between light and dark side powers, and characters are penalized for attempting to use the powers that do not match their alignment.
KotOR and KotOR II do, however, promote alternative philosophies about the Force and subject Jedi norms and beliefs to fierce scrutiny. The way it most contributed to the concept of the Grey Jedi is via Jolee Bindo, who is evidently a good person opposed to the dark side but is expressly given neutral alignment because he became an outcast of the Jedi Order and defied their oppobrium against romantic love.
This highlights one of the original reasons for the concept's popularity: its conflation of the light side with the Jedi Order. Conformity with Jedi ideological practices was misinterpreted by many fans as the prerequisite for being a light-sider. In part, this probably stemmed from the in-universe pejorative usage of the label to brand unorthodox Jedi like Jolee Bindo and Qui-Gon Jinn, even if they are steadfastly in the light. Fans saw the Jedi and the Sith as polar opposites and, committing the golden mean fallacy and the false dilemma fallacy, argued that they were extremes of equal moral weight such that the most ethical route was actually to be "balanced" between them.
The other reason for its popularity is what you guys have already pointed out: the desire to live the power fantasy. Some fans wanted to be able to use cool dark side powers like Force lightning in their imagination while still reserving the right to be a light-sider. As I said, I don't think this reasoning was promoted by KotOR and TFU. It goes back further to at least Jedi Knight: Jedi Academy, where Kyle Katarn instructs the player that no powers are inherently light or dark and what matters is only how we use them. I always suspected that the writers of this (and related ideas in contemporaneous works) were inserting their distaste for the moral objectivist framework that the dark side's existence implies. As well, they wanted a justification for a more ethical egotist value system to be legitimated in the lore concerning the Force.