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.)
Apparently that speed up was originally a bug https://www.svg.com/293293/details-you-didnt-know-about-space-invaders/