Is it unethical to submit a paper without addressing criticism?
Maybe. I lean towards "yes", but it is complicated.
On the one hand, if one journal does not accept a paper, but the authors are confident of their results, then it is entirely reasonable to resubmit the paper elsewhere. This really isn't a problem, in and of itself.
On the other hand, if an author submits a paper to a journal, and the reviewers point out perceived errors or flaws, the burden is on the author of the paper to either correct the errors (if they are "legitimate" problems), or rebut the reviewer and explain why the perceived errors are not a problem. Until the problems are either corrected or rebutted, the assumption should be that the paper is flawed.
If the author resubmits the paper somewhere else without fixing the problems, they are engaging in a kind of deception—they are presenting a flawed paper as though it had no flaws.
Additionally, this reeks of something like p-hacking. Whenever you submit a paper, there is some chance that it will be accepted, even if it is flawed. The more times you resubmit the paper, the more likely it is that some journal, somewhere, will eventually accept it. It is like rerunning the same flawed experiment over and over again, and only keeping the result which, at random, rises above your desired significance level.
Don't do it.
Is it productive to submit a paper without addressing criticism?
No. Absolutely not.
Even if you are being selfish, this is a waste of your time (not to mention the time of the reviewers and editors who have to deal with your paper). Academic circles tend to be relatively small and, depending on how broad your field is, it is likely that you will encounter the same reviewer over and over again. This reviewer will point out the same perceived flaws over and over again. This doesn't help you to get your paper in print.
If your goal is publication, address the review. Explain why their criticisms are incorrect, or edit the paper to fix the errors.