>It'd help your case if you gave us some examples of such scripts being used.

I want OP_CAT so that I can securely and compactly verify many hashes and hash preimages. This would shrink offchain Tumblebit transactions significantly.

For instance if I want a transaction TxA which checks that a transaction TxB releases preimages x1,x2,...,x10 such that

y1=H(x1), y2=H(x2),...,y10=H(x10). Currently I just put y1,...y10 and check that the preimahes hash correctly. With OP_CAT I would only have to store one hash in TxA, yhash

ytotal = H(OP_CAT(H(OP_CAT(y1, y2)),y3)...y10)

TxA could then just hash all the preimages supplied by TxB and confirm they hash to TxA. This would reduce the size of TxA from approx 10*32B to 32+10*16B. I have a version which improves this further but it is more complex.

Most of the math OP codes aren't particularly helpful due to their 32bit nature and their strange overflow behavior.