Hold onto your balls, because you're about to get blasted.
He rode Cobain's coattails? Grohl was the drummer in Scream, one of the most influential hardcore bands in the 80s before he was in Nirvana. Then, when he joined Nirvana, on the recommendation of King Buzzo of the Melvins, the band who influenced Cobain the most. He gave Grohl's info to Novoselic, who flew him to Seattle, tried him out, and essentially begged him to join the band
While in Nirvana, he actually contributed to a majority of the songwriting on the Incesticide EP and In Utero. He actually wrote two full albums before Nevermind came out, but was afraid to let Cobain and Novoselic listen to them because he didn't want to disrupt the bands chemistry or success.
And after all of that success, he founded the Foo Fighters, which has been arguably the most influential rock group over the last 20 years in pop music. He also released an album as the drummer of Queens of the Stone Age, his horrifically underrated and critically acclaimed Probot solo metal project, and the super group Them Crooked Vultures, which paired with him Led Zeppelin bassist John Paul Jones and QOTSA/Kyuss guitarist Josh Homme.
Oh yeah, and he's won 13 Grammys, only one of them coming as a member of Nirvana (and it was actually their Unplugged album that won it, something that was released after Nirvana broke up). Yeah, it sounds like Grohl really rode Cobain's coatails.