If we hold that by a Sakana we make a Yom Chol, then Rav Papa has no proof from the Mishna. The reason we do this Refuah is because we are already doing Refuos.
If we assume there is another reason for Metzitza then what Rav Papa is saying is that since this part is even done on Shabbos it must also be because of Sakanah. This is why he didn’t mention the other stuff.
It seems like in the times of the Amora’im they must have already had issues with Metzitza.