FWIW, I would try and fight that "no need for physio" recommendation. Full range of motion is, as you note, not the same as full usage. If you wait a few months you may find that you've compensated in bad ways for the strength loss and then find it more effort to recover. To compare, I had a clean break, no pinning. Started physio 6 weeks after the break, was onto full weight press ups by 11 weeks post accident, and back climbing after 15. My experience was that focussed rehab exercises really helped that along (had previously dislocated the AC joint in the same shoulder so was expecting this).