How about actually live, rather than live recordings? I am sure most of us have heard a lot of songs played live that we can’t name, but I can name a couple.
In their early, pre-Bowie-influence days, Mott the Hoople use to encore with an instrumental version of The Kinks’ “You Really Got Me”. I heard them do it about 3 times. It does appear on, I think, their first album, but I have never heard that (presumably studio) version. I can’t imagine that it would work very well on record, whether it was a studio performance or a live recording, but it was terrific as the climax to their very energetic and exciting stage show - rock and roll stripped down to its bare minimum! Like punk in its simplicity and energy, but joyful rather than angry.
The last time I saw them, it was shortly before they finally had a hit with “All the Young Dudes” (Mott was expected to be the next big thing for a couple of years before that finally did it for them). Their act had changed quite a lot from the previous times I had seen them, and to my disappointment did not do “You Really Got Me”. I don’t think they did “All the Young Dudes” either, but what they did finish with was an odd version of “Mr Tambourine Man” that substituted bugle player for tambourine man. (I have no idea why.) I don’t think there is a recording of that, or if there is, I have certainly not heard it.
Coming back to live recordings, the whole of John Mayall’s brilliant The Turning Point was recorded live. I do not think studio versions of any of it exist. Also, probably all of us have only heard The Beatles’ “Get Back” and “Don’t Let Me Down” as live recordings from the rooftop concert. (Do these count, or does a studio version have to exist?)
The Doors Absolutely Live contains several songs that AFAIK they never released studio versions of, notably the notorious “The Celebration of the Lizard”. A studio version of part of it (that I have heard) is on their Waiting for the Sun album (IIRC), but it is far from the whole thing. I think that, technically, I also heard “The Celebration of the Lizard” live in concert, at the Isle of Wight Festival in 1970, but I was so far away from the stage at that point that it all sounded really quiet, and lost all impact.
Like most people, I have never heard the studio versions of the Frampton Comes Alive hits. However, as well as the once ubiquitous live recordings, I have also heard him play them live - at the L.A. County Fair in about 1998 (give or take a year or two).