Alex Niven chimes in, offering the equation of "Drumming in pop: shittier = better." As far as rock is concerned, I admit I favor that aesthetic; or I do about half the time. Which brings to mind another favorite of mine, quite different from the prior nominees...
In their day, the Velvet Underground were reputedly considered by many to be the most wretched band in existence. Or they were as far as most people were concerned. A fair amount of this had to do with their art-damaged experimentalism, which many considered an offense to the ear. But there were also charges of gross musical incompetence, and many of those allegation of ineptitude were directed at drummer Maureen Tucker.
The above is anatypical VU number, which may be why I've always liked it so much. An instrumental outtake belatedly made available to the public in 1986, it's as raw as the vocal version of the tune that had circulated in bootleg form, if not a little moreso. But definitely faster and more crazed. It's a raging garage banger, or the incessant sound of banging inside of a garage, a pounding that rattles all the tools off the walls. Brute, merciless sonic minimalism of the most wonderfully primitive sort. Reed's rhythm guitar, Cale's bass -- the entire band is banging away in strictly percussive mode, an engine firing on all pistons, save for the occasional sidestep of Sterling Morrison's yakkety blues-tinged soloing. All with maximal fuzz-tonage. But it's the drumming -- there, in the center, the swollen heart of the thing pounding furiously and tirelessly away -- that always puts a smile on my face, all but makes me laugh with idiot glee sometimes.
But I guess it could be argued that the idea of a chugga-chugga musical-combo-as-(strictly)rhythm-unit was pretty much what rock'n'roll was all about in the first place. Case in point:
...The original version of the tune "Bo Diddley" (the one w/o the "Hey...,") having been perhaps be one of the greatest rock'n'roll records ever, or at least the best rock'n'roll drum song ever recorded.
And maybe one could split minimalistic musicological hairs and argue that the above are contrasts in centrifugal versus centripetal force. Dunno. Whatever.