When you listen to Keith Richards' 1988 demo of Almost Hear You Sigh, you can see why he was holding back from putting it on his solo album, Talk is Cheap. It was good, but it wasn't great. It had a groove, but it wasn't groovin'.
It needed Mick, for sure: Jagger would add his vocals and blag a co-write. But, more importantly, it needed Charlie's drums; Mick and Keith don't make the Stones. Mick + Keith + Charlie = the Stones. Elementary.
Sans Charlie (1988)
Avec Charlie* (1990)
Criminally, they only ever played it live a handful of times (on the Steel Wheels tour in 1990). It was then put away in a bottom drawer where it resides to this day.
* Also contains a most exquisite Spanish acoustic guitar solo from Keith.