All great comments. As always, taste is personal. For instance, I love Bonham's snare sound (a 6.5" deep metal Ludwig shell), but hate Chad's (that high-pitched wood piccolo sound).
What constitutes over-playing is a matter of opinion. The tale I have told before bears repeating. Master guitarist Danny Gatton, after a few songs into the first gig with his new drummer, had the following exchange with him:
Danny: "You know that fancy stuff you're playing?"
drummer: "Yeah."
Danny: "Don't."
Bonham's playing absolutely works in Led Zeppelin, the same way Keith Moon's does in The Who. Neither could have played on the Aretha Franklin recordings Jerry Wexler produced in Muscle Shoals, which feature the great Roger Hawkins on drums. And Roger's playing would not be appropriate in Zeppelin or The Who. It worked awfully well in late Traffic, though. Horses for courses.
One more thing: Taste, economy, and lack of over-playing need not restrict a drummer to playing nothing more than keeping time, playing only the 2/4 backbeat and four-on-the-floor bass drum patterns. Do yourself a favor and listen to Levon Helm's playing on the first Band album, and his and Band pianist Richard Manuel's (he's a very creative, really inventive and interesting drummer) playing on the second. And for really wild, off-the-wall playing, Earl Palmer on the many early Rock 'n' Roll recordings he played on---Little Richard, for instance. He swung like mad, and had chops to die for. NOBODY played like Earl!