I believe The Beatles: Rock Band came the closest to being perfect. Eveything about that game was just beautifully done and the only things missing was Pro Drums, an option for Keys, and a few more Beatle songs (Hey Jude, Strawberry Fields Forever, Yesterday etc. etc.)
I still need to get around playing the DLC but I feel like I’d need to watch a video to get caught up on the story. That said, yeah, the gameplay and story is absolutely incredible. Perfectly-executed mystery box.