The big advantage when you record the final composite in real-time is (of course) that the workflow is much much faster. This is the perfect world for virtual production.
However, it can make sense to do the greenscreen keying in post production.
In the following scene I used the real-time composite to see my final picture while filming, but I did the real keying work for the final product in Post Production. It took much longer to render everything out and sync it, but I was able to keep the green bag and green parts of the artists top that the artist wanted to keep in any way!! 🙂