I finished a carbon steel knife on a Suita stone a few weeks ago. I TPT-ed the edge and I felt it was biting, similar to a freshly set bevel on a razor, after 1K. I stropped that knife, and the bite was almost gone. I repeated that exercise, because I was using the knife and dulled it, checked again, same again.

I cannot imagine not stropping, but then again, I am not able to reproduce the scenario in question here. All I can say is, the strop always helps in my case. I often try the edge on my face after the finishing stone, and it's never as good as the stropped edge.

I have also not experienced any such thing as an overstropped razor. I am making some strops now and I used a single shave-ready razor to test the leather. Must have stropped that blade a 1000 times over in a single day, then I shaved with it. That was a very good shave, indeed.