Simple snowball effect.
He had a RPG setting named after his story, so he got the most attention. In time, more corporate folks got the idea of “Hey let’s market the shit out this guy!” and so now he’s the most recognizable and is basically the face of the eldritch horrors. Even if it isn't directly Lovecraft related, squidface still pops up as an influence for something similar (Mass Effect Reapers, D&Ds Mind Flayers, etc)
Also, while he’s not the most powerful, he has somewhat of a recognizable form. Something like Azathoth or Yog-Soth are usually described as incomprehensible to the human eye (hence all the madness) and I suppose it would be a pain in the ass the draw those fuckers all the time especially when each artist would have their own idea of what it might look like.
But, yeah it was just a roll of the random cosmic dice (which seems appropriate given the mythos) that Cthulhu got all the credit. It could have easily been Dagon, Hastur or Chuzzlegoozlewog.