If a particular piece of work is utterly terrible, with no redeeming qualities whatsoever, criticism of that work need not be constructive to be valid. People can also read criticism and decide whether or not they agree with it to form their own opinion, irrespective of whether that criticism was constructive.
If nonconstructive criticism were valid no one would ever improve or want, I could just tell you that "you suck" or "did a lot of things wrong" what will you know what or how to improve if I don't tell you what the problem is? I'd argue that person needs to improve at constructing their criticisms.
Unconstructive criticism is not valid because it is just an insult. If no lesson can be learned and no improvements can be made from a piece of criticism, then there is no good reason to express it. Insulting people's work will only cause disputes and will make the goal harder to achieve in the end.