I haven't heard any good recordings made by dead people:))
On a more serious note - what constitutes a "live" recording?.ย Many classical and jazz recordings made in studios are "live" in the sense that they are played in real time albeit in the absence of an audience - though, admittedly, there may multiple takes and some post production editing. That said, lots of "live" recordings are edited too.
As for rock and pop recordings, most are recorded using a feed from the mixing desk, so they are not what the audience heard via the stage / PA, with perhaps an element of feed from the PA / hall mixed in for atmosphere.