The physical body - and the physical environment we live in - are just variables that can be gradually altered. Even if the brain is optimized towards a particular environment, it doesn't mean it won't handle a different one.
They do exists as beings, yes, but different beings than the ones who possessed (or would have possessed) those limbs.
The question is not one of necessary conditions for "being-hood", it is one of identity via continuity.
As for being a different being, I personally wouldn't mind. I'm not the same being I was yesterday, or last year, anyway. For instance, over the past few years, I have many parts of my teeth removed and replaced with artificial components. I do not feel worse because of that.
At what point are you not you?
Bionic organs? limbs? New bones, artificial blood? Neuro-prosthetic interfaces or implants? "Biologically integrated coprocessors"?
I'm Genuinely curious where you choose to draw the line since it's not often discussed from a personal standpoint it's usually just the philosophical arguments that get discussed in what I've read.
Creating an exact copy of me wouldn't make me experience the world from two different perspectives at the same time. It would just create a new human being that, allegedly, would be a "copy" of me (or so people would say).
To me, it would just be another person walking around. There wouldn't be any essential difference between this person and an adult child of mine.
So if you kill the original - maybe because the procedure is destructive or because it's a consciousness-saving emergency measure - the "copy" would have a pretty good claim to be a continuation of you.
But I'm not interested in legacy style immortality. I don't care at all if a separate version of me continues to exist – I want to be continuous with the physical substrate I now occupy. In other words, we are all Ship's of Theseus, and that's fine, but a perfect replica of the Ship breaks my internal narrative of continuity.
To distinguish: If a form of "immortality" supports the possibility of another copy of me existing simultaneously with the current incarnation, then it is not the immortality I'd desire.
Responding to the parent, I would much prefer slowly replacing my neural hardware with circuitry to wholesale scanning and instantiation in another substrate.
Summarize: Identity is (partially) a function of substrate. Change the substrate in a discontinuous fashion, and identity itself becomes discontinuous. I call that discontinuity (one form of) "Death".