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I just finished reading OS and it is interesting that they do not find it necessary to do stretching and mobility. Perhaps it has merit to it that if you only do OS then you might not need to stretch or mobilize joints.It depends
I stopped stretching and doing "classic" mobility work about a year ago. My mobility and stability has improved and became more consistent over that period. But that does not mean there is a cause and effects (no stretching -> better mobility). My main lift is the bent press, I do allot of OS work, sleep without a pillow, sit on the floor, I do loaded mobility (armbars, light getups, goblet squats), carries, crawling, some club work and finish practice sessions feeling stronger than I started.
So, is dedicated stretching necessary? Personally I don't think so. I think general joint alignment and health and mobility and control are a must. The specific tool used is, like any tool, depending on various things.