Ahhh Fripp.
I've been a Crim fan, with Fripp, the musician, at the core of my Crimsophelia. However, my favorite eras are those from Court up to Discipline. I find it kinda funny for Fripp to have said this of Bill, in consideration of how intensely Michael Giles, Andy McCulloch and Ian Wallace, all tended to play - although I enjoy most every bit of it.
With the advent of Bruford and Jamie Muir, those Lark's Tongues rhythmic textures do get quite thick, but mostly due to the two of them playing. I find Bill alone to be some what balanced in his use of note and space, albeit rhythmically complex in context of the rest of the music. (His drums on Close To The Edge seem a case in point - some very inventive yet simple playing in contrast to the rest of the music.)
Yet with Fripp gearing toward 2 drummers so much, as well as the whole double-trio thing + soundscapes... all at the same time - his statements almost seem oxymoronic, don't they? Although I do undertand everything he says from his teacher point of view.
I suppose it depends on the era in which he made the list re: Bill.
As for the original post topic - I like drummers who are musicians - not just drummers as exclusive, genre pointed instrumentalists - though I like those, too for style specific gigs.
But for personal music, I like players with a sense of scope, stylistically, historically, musically - who like diversity, are happy to play super simple (like Bruford's slit drum on "The Sheltering Sky") to mayhem - like Keith Moon - who seems to very much play off of the guitar and the drums and the vocals and the voices in his head
But flexibility is key, along with a confidence that is both able to follow and lead, but in the context of listening and paying attention to all of the music.
I've worked with drummers where playing softly means slow down to them, (Bruford is a master of quiet intensity). And yet with others where, if they can't hear well or distinguish what the music is doing, that they feel it is their job to drive it into control - and sometimes wrongly so. If you can't hear what the rest of the band is doing - play quieter, look, listen and follow, unless someone gives you the signal to go for it.
But much of this all depends on the genre of music. I like music with an "orchestral" character, not big, just using instruments for the sake of color and illustrating the core emotion and intent of the story - whatever that takes from nothing to everything. And it doesn't take a big drum kit to do that, just an inventive musician who speaks the language as a drummer.