We need to put ourselves in councillors' shoes, and those of the developers and drivers. What would be lost by going to the Sustrans design? And does it make things untenable?
I'll give this more thought later, but things that spring to mind:
Developers need people to be able to access their massive car park (and the one at Greenside). May not be popular here, but it's happening. Sustrans design allows for that, if you are coming from the north/east. Reduces access from the Bridges (but that's not insurmountable in my view - anyone approaching from south of the university could go via Abbey Hill. [What they should have done is an underpass from the London Road roundabout under Picardy Place/Plaza to the car parks, but too late for that.]
Cars heading from Leith Walk/Broughton to Southside: inconvenienced but again would soon learn to go via Abbey Hill or up the Mound or Lothian Road, depending on their destination.
Cars heading Leith Walk to West End: would come up a against a set of traffic lights at Broughton St. There is a set of lights there, but they're for a ped crossing, so there is likely to be a longer wait which will back the junction up a bit. However, reduced use of Leith Street due to bus gate may mean that the overall effect here is limited.
Broughton Street: already traffic light-controlled, so little impact (beyond induced demand due to St James development, which is going to happen anyway).
A Picardy Place plaza presumably limits what can be done with this notional hotel possibly planned (if the common weal issues don't sink that anyway). Is anyone bought into that, beyond the council thinking it could raise some income for it?
etc...
I can see the bus gate/closing Leith Street being the big issue because WE FEAR CHANGE, but surely not insurmountable? The upside of reducing traffic on the Bridges/Leith Street is surely a good thing as long as you accept that some (not all - people will be encouraged onto buses/foot/bike) of that crosstown traffic will move to the Mound/Abbey Hill/Holyrood Park/Lothian Road...? And a Plaza as the entrance to the St James Centre/the new hotel/Omni is good for footfall/business.