Which is why
I always liked Ringo, especially in the later years. Predictable, sure, but an integral part of the sound. That's the same reason I enjoyed Ginger Baker in the Cream days: you knew what he was going to do, but he did it so well...
Keith Moon is another fave, same reason, entirely different sound. And you cannot cover "Happy Jack" going light on the drums. Nor "Miles and Miles", come to that.
I played drums in that era myself, in garages and basements. Not since.
Getting back to the tastily blended-in drummers... I nominate Levon Helm of The Band.