It was never a matter of “the west”. The See at Rome was respected and Orthodox. More than enough reason to ask it to arbitrate.
What is it about this authority that we don’t have right now?
We always have a primate to adjudicate for us if we need that. Now as then it was always a matter of mutual respect between the parties and respect for the facilitator.
What we did not have, ever, was the See at Rome naming bishops for us, or regulating our liturgies, or canonizing our saints, or declaring our dogmas. Those things we have always done either within our own synods or gathered in council. We don’t need a Pope for that.
If we did need a Pope, there would have been a lot of scrambling around after the schism making new canons to deal with a changed situation. Check the historic record, there was nothing like that. It isn’t like the Orthodox were at a loss about what had to be done and how to do it without a Pope. There weren’t even any discussions.
There was no crises, because the Pope literally did nothing. In the east it was business as usual. Most Orthodox probably didn’t even really understand the implications of the schism until the crusades, when foreign armies were marching across the land and arresting or expelling the Orthodox bishops.