I'm really not a fan of great performances. Iconography and cults of personality. Fuck that shit. So I hate great live albums.
Not quite sure where you're coming from with that argument. Great performances and great live albums aren't quite the same thing. There's loads of performances that people who were there rave about, but don't come across on a live album - are there any absolutely essential Bowie live albums?
Live albums can work for all sorts of reasons.
Like The Cramps' Smell of Female - as you listen to it you can feel the sweat drip from the ceiling, Lux Interior's asides to the audience feel like they're directed to the person bopping next to you, it puts you in the Peppermint Lounge for a riotous gig.
Or Jerry Lee Lewis & The Nashville Teens Live at the Hamburg Star Club - Lewis powers through those songs with such furious abandon that it makes the iconic original studio recordings sound like nursery rhymes.
Or Fania All Stars Recorded Live at the Red Garter - a performance by a crowd of many of the best US Latin musicians, most of whom are a decade or two into their careers, bringing together the many styles of Latin music - pachanga, cha cha, guajira, son, montuno, guaguanco, danzon, boogaloo - and right there on the record creating a new scene, a new sound - salsa. You're listening to musical history.
Sure, they are all great performances, but a great live album needs more than just that. And like you say, a great live album doesn't even need a great performance at all.