This album, and The Beatles, are victims of their own success. They're so good now that they've become bad. When you think of The Beatles you no longer think of their music but what they represent - success, raging fans, wild popularity. But if you can disassociate those from the music then you might hear why The Beatles became legends in the first place.
This is my favorite Stones album and quite possibly one of my favorite albums to listen to, from start to finish, bar none. There are any number of reasons for this, one of the major ones being the right marriage of band and producer (Jimmy Miller). Every passage seems pre-planned for maximum effect, and yet, every time I listen to the album I come away mind-blown at how effortless and natural the whole thing comes off.
Another point - the musical flow of Let It Bleed is immaculate. Nothing ever feels out of place, out of left field, even where you could argue "Honky Tonk Women" should go in the slot where "Country Honk" is at on the record - guess what - "Honk" was the original take, so this ramshackle thing feels just as right as the massive bookends which start and end the album.
And the sad irony? It was released two days after the Altamont debacle.