Best Live Album Ever...

There are some excellent suggestions--I'd add B.B. King live at the Regal.
Those BBC "live" recordings, while usually great, are often really studio recordings, sometimes with overdubs. The Dire Straits and perhaps Led Zeppelin tapes are exceptions. Pretty sure the Beatles were "live in the studio" with no audience and in a very controlled situation.

Hendrix in the West

Aswad, Live and Direct.

Spyboy (Emmylou Harris, Buddy Miller, Brady Blade, Daryl Johnson)

The live portions of Wheels of Fire, Cheap Thrills, and Undead (Ten Years After)

Bless Its Pointed Little Head (Airplane)

Frampton Comes Alive!