I agree, this is a common format I've experienced in academia.
For what it's worth, I've found that it sometimes evolves into unnecessary criticisms of the paper, and sometimes the criticisms aren't really correct (i.e. the author isn't there to defend the method and perhaps the presenter hasn't quite understood the paper or reasoning themselves).
I've started to believe that this reading group format might actually contribute to why a lot of PhD students feel so frozen/overwhelmed when writing papers of their own... they watch perfectly fine papers get ritually dunked on once a week, and then those criticisms get embedded into their inner critic and sabotage their writing progress! :-)
Well done, Sam, this is really helpful - thank you!