I read the following in this paper (Otmar Spinas, Proper products. Proceedings of the AMS, 137 (8), (2009), 2767–2772):
$ \mathbb{L}^2 $ adds a Cohen real. Thus it was considered uninteresting from the forcing point of view.
Why is that so? (I mean the latter sentence, not the formal statement.)
Some suggestions:
Cohen forcing is a fairly well-understood and studied forcing notion. To say that $\mathbb L^2$ is "uninteresting" could simply mean that we end up with a notion of forcing about which we already know all there is to know. (Though, of course, this is an exaggeration.) However, I do not quite buy that this is the sense in which the comment in question has been made, since $\mathbb L^2$ is not equivalent to Cohen forcing, and the quotient $\mathbb L^2/\mathrm{Cohen}$ could still be worthy of investigation.
Rather than the above, I believe the comment was made in the context of how Laver forcing itself is used. Recall that $\mathbb L$ was introduced to deal with the Borel conjecture, showing that it is indeed consistent that the only strong measure zero sets are the countable sets. On the other hand, Cohen forcing forces that the ground model reals form a strong measure zero set. This would suggest someone who has studied $\mathbb L$ that $\mathbb L^2$ does not share the key properties of $\mathbb L$ that were the reason to study it in the first place. For an analogy, consider a Suslin tree $\mathbb S$ as a ccc forcing notion and compare it with $\mathbb S\times\mathbb S$, which is not ccc. If for some reason one is working in a context where only ccc forcings are being considered, this would make $\mathbb S\times\mathbb S$ a forcing poset that one may discard. $$ $$ The following quote from Blass's Handbook article (available here) on cardinal characteristics suggests that this is the sense in which the comment was made:
There is a third option, that I skipped originally since I figure Andreas or Arthur would address this point better than myself, but at least mention should be made of it. Namely, it may be that the interest in the forcing is from the point of view of its effect on the cardinal characteristics, and the presence of Cohen reals presumably trivializes the combinatorics on the continuum present after forcing by $\mathbb L$. It is not too clear, though, that the addition of Cohen reals destroys all interesting relationships in the Cichon diagram since, again, the quotient $\mathbb L^2/\mathrm{Cohen}$ is non-trivial. (As far as I can see, it is not that $\mathbb L^2$ factors as $\mathbb P*\mathrm{Cohen}$ for some $\mathbb P$.)
Very related (and this is why I mentioned Suslin trees and the failure of ccc in the product) is the issue of preservation of properness, that is the content of the paper. As explained there, $\mathbb L^\omega$ fails to be proper, and this is due to the addition of Cohen reals. Anyway, I find the remark too ambiguous. As a referee I would have asked Otmas to clarify very explicitly what the comment meant, or to remove it altogether.