Back when paper tickets and e-tickets were coexisting if you had open dated segments, AA and others would issue a paper ticket. After paper tickets went away, I had some long discussions with the AA and BA rtw desks about open dated segments on xonex e-tickets and both refused to even consider booking with open dated segments (CX also refused open dating for xonex tickets). I finally gave up. I would be quite interested if anyone has successfully obtained an xonex e-ticket with open dated segments recently.

Edited to add: I know that Amadeus allows open dated segments (although finding an agent to do it can be difficult) but, iirc, making these open dated segments work across one GDS to another (specifically, Sabre) was the reason OW members seemed to reject booking open dated segments.