I find this attitude on code reviews to be extremely demotivating, especially on code bases where I am not the primary committer or lack overall responsibility for the system being changed. It completely distracts from the code under review, and it only requires a small amount of social/organisational ill health to be abused.
Even if you believe that the next committer should clean up, it can require quite a big context switch - either the clean up explodes into quite a big task and you have to question the trade-offs being made in doing it now, or it doesn't have full focus and becomes risky and/or no real improvement.
I don't happen to believe that the next committer should clean up in most of these situations. Minor things, sure, you should do it (but don't side-track the review with it!). In my experience, people who already couldn't be bothered to do it or clean up later use a new commit as an excuse to get their work done for them. I've often seen people criticising tangential code issues in review who were responsible for the original commit. The question becomes - if it's such a minor issue for me to clean up, why wasn't it a minor issue for you to clean up? If it's bigger, how did it pass review in the first place?
My view is that extraneous cleanup should be proportional to the original change at most - and not discussed in code review of unrelated changes. If a particular area of the code sees sufficient churn to accumulate more and more debt, everybody will know and talk about it, it will be clear that some specific refactoring is necessary, and more importantly it will be evidence that small cleanup is worthless (high churn) and a better architecture is valuable (high churn). A given team may have high tolerance for technical debt and thus never do this work. But then they are screwed anyway, why create noise at every review just hoping that someone else solves it?
Remember, there's also a good chance that the mess stays the same as it always was, sitting there passively. And there's a chance that the cleanup introduces unanticipated problems, especially if it's legacy code with no/less testing.