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Really? But why? All of 2+2, 2*2 2^2 are trivially 4, and sqrt(4)=2 so why is the + more odd than others?

Because sqrt is the reverse of 2^2 and 2*2 (which is 2^2 unwrapped). Though there's no direct relationship between sqrt and 2+2 other than that it happens to be equal to 2*2.

Or put differently: N = sqrt(N^2) or sqrt(N * N) for every positive N, but x = sqrt(x + x) or sqrt(x + 2) is only true for x = 2 for both or x = 0 for the first representation.

If 2*2 is 2^2 unwrapped, then surely 2+2 is 2*2 unwrapped, thus 2+2 is 2^2 unwrapped^2 and is also natural via transitivity? :P

Though as I said in the rest of my comment, the 2+2 unwrap only works for N=2. So it's not a general unwrap, but rather a specific example that happens to work for N=2.

The 2*2 also doesn't seem a general unwrap.

2^2 -> 2*2 -> 2+2

2^3 -> 2*2*2 -> (2+2)+(2+2)

It's not N^Y, it's N^2 as we are talking about the reverse of sqrt which is N^(1/2).

N^2 == N*N != N+N

N^2 = N*N = Sum_i=1 to N of N.

More generally "unwrap" is being used as inlining the recursive hyper operation once more: https://en.wikipedia.org/wiki/Hyperoperation

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