A teacher friend of mine always goes through his stack twice. Once to correct all mistakes and a second time to write down points. As you said, once you have seen all mistakes you know how "bad" of a mistake it actually is.
Crucially, this is not quite what the poster said. It’s not about stack ranking students against each other.
Say every paper makes the same subtle mistake, and you only notice it halfway through the pile. Unless you go back through them all, you’ll unfairly grade the later entries more harshly.
It's not, but it sort of has that effect, albeit indirectly, and definitely unfairly.
If you weigh the severity of students mistakes (or successes for that matter) in relation to each other rather than to an objective rubric, you’re effectively stack ranking them whether you mean to or not.