Is there anything better than live recordings?

Unplugged Nirvana, Eagles, Clapton, Zep’s BBC sessions, Zappa’ New York, Roxy, A night in SF, Jazz at Pawnshop, Live at Leeds, Deep Purple Made in Japan, Talking Heads The name of the band, Portishead Roseland NYC, Belafonte at CH, China Jean MJ, Kraftwerk Min Max, Tangerine Dream Ricochet and Encore, Laurie Anderson Home of the Brave, are some nice examples. Then you have the ballets, Swan Lake, Romeo and Juliet... opera, classical in general but these cannot be performed in a studio.

Generally a very few number compared to studio releases (contemporary).

How can i forget this, King Crimson Absent lovers, but only on CD.

Think it that way, two different worlds, one is a love letter the other a hot date.

I much prefer studio rock recordings to most live ones.

Much depends on engineer, group, as many times they set up microphones and sound only relying on soundcheck without putting into account, the audience, microphones moving from original positions, the lighting, and many more.