You can already write a Rust program that never relies on Copy, by explicitly calling .clone() whenever you need to copy something. It's just that this would be insane.
`.clone()` is usually implemented in terms of `Copy`, but the real problem that I don't know how to solve without `Copy` is the use of references. Every time you call a function on a shared reference (including the one used by `clone`) you are implicitly copying the reference. It only works because of `Copy`. Without it, I think you would need unsafe code or something in order to call a shared method and retain access to the original reference, which would pretty much no longer be Rust since the vast majority of methods wouldn't be correctly expressible in the safe subset. There might be reborrowing style tricks you could use to get around this, but as you said the "core" of Rust shouldn't have reborrowing. Or maybe you could implement clone on references in unsafe code and then just explicitly take a reference to the reference every time you needed to duplicate it... There is also the linear type trick you can use to copy a value by pattern matching it destructively, explicitly enumerating all possibilities, and then generating a fresh product with each possibility listed twice, but that cannot implement copy for references.
In any case, I think it's just true that `Copy` is quite fundamental to Rust. IMO even if you could somehow turn all instances of it into syntactic sugar (which I think is not true, as the `Cell` example shows), the surface language you used would be sufficiently unlike Rust that it wouldn't really be Rust anymore.
Well no, some objects (notably Cell<>) require Copy, because clone(&self) takes a reference and can do arbitrary things with the Cell (including overwriting the data its ref points to via Cell::set())
