Yes, but the hashing of the merkle tree to obtain the merkle root takes like 10^4 hashes for 10^3 transactions.
Compared with 2^80 that is about the number of hash operations needed to find a POW block header, it it trascurable.
Did i get this wrong?
Numbers i said are my guesses, but the order of magnitude should be about that.
I don't remember exactly how many hash ops you have to do to put 1000 txes in a merkle tree, but it should be more than 1000 and less than 10000.
My point was exactly that. Computational cost of the merkle tree is negligible when confronted with the computational cost of the POW