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 picked up Fata Morgana a few months ago, at the same time as Steins; Gate. But so far still going through SG (I enjoy VNs but it takes me so long to play them compared to other genres)…
Anyway, I appreciate you mentioning it here, it reminds me that I want to play this one soon!