IMHO, the emotion and spontaneity projected from a great live album is unachievable in a studio album. Studio albums can project perfection of the performance and virtuosity. There are so many great live recordings that have been covered earlier, there are many more beyond rock in jazz and blues as well.
My two favorite live albums are The Name of this Band is Talking heads (1982) and Bob Marley and the Wailers, Live at the Roxy (2003). Both, with no or little compression and energy through the roof. They are played very loud (90+ db at your listening position - haha).
Maybe we should compile a list of our top 5 favorite albums?