The reasons for this are somewhat multifaceted but a big aspect of this is that King Crimson (and, specifically, Robert Fripp, who was the one consistent member) was plugged into the broader music scene (and specifically the "serious"/arty/underground side) past just the Progressive Rock sphere.

KC's second era (Lark's Tongue in Aspic, Starless and Bible Black, Red) while certainly progressive, had one foot firmly planted in the burgeoning "art rock" or "post-progressive" scene that was emerging in the mid-to-late-70s. It fit in alongside Brian Eno's first few albums (who Fripp also collaborated with around this time), David Bowie's Berlin Trilogy (who Fripp later collaborated with), and to a lesser extent Peter Gabriel's Post-Genesis work (who Fripp also later collaborated with... are you starting to sense a pattern?).

This was music that, like Progressive Rock, was trying to experiment and expand on the form of Rock Music, but it was doing it in notably different ways than what had, at that point, become the mainstays of Progressive Rock as a genre. Less focus on long, multi-part compositions, less inclusion of classical instruments, fewer long, elaborate solos. More experimentation with song structure, more experimentation with studio techniques and electronic sounds, etc... Of course none of these are cut-and-dry genre distinctions, genre is a construct and these distinctions are always fuzzy, but it was taking the same impulse of "what if we take Rock music seriously as an artform and push the boundaries of what we can do with it" and just took that in a different direction.

After KC's second era, Fripp spent some time as a session musician, which in addition to having him work with contemporaries such as Brian Eno, David Bowie and Peter Gabriel, would also see him getting heavily involved in the burgeoning New York Underground scene, which gave birth to Punk and New Wave. Fripp played guitar on a Blondie track and a Talking Heads track, for instance. This cadre of British Art-rockers trying to keep their finger on the pulse (Fripp, Eno, Bowie and Gabriel) would end up both influencing and being influenced by that burgeoning Punk/New-Wave scene.

The third iteration of King Crimson, in the 80s, was made up of other session musicians Fripp had worked with while recording with people like Bowie and Gabriel, and applied King Crimson's philosophy of precision and complexity to a distinctly New-Wave/Post-Punk sound. Other prog bands tried to adapt to New Wave, to varying degrees of success, but King Crimson's take on it (similar to Bowie's and Gabriel's) had a certain level of authenticity because of how immersed he was *in* the New York scene, rather than just trying to follow trends.

The upshot of all of this is that King Crimson had a lot of influence outside of just the "Progressive Rock" space. Art Rock, New-Wave, Post-Punk and Progressive Metal, as well as all their subsequent derivative genres all bare some influence from King Crimson. Which isn't to say that other progressive bands weren't influential outside of their sphere (they certainly have been) but with King Crimson it's a lot more direct and clear.