" Interested to hear people's thoughts."
My thoughts are that there shouldn't be any junctions in Edinburgh where the options available to bikes are limited. The restrictions are there entirely for the purposes of 'traffic flow' so bikes shouldn't be constrained by rules which are not intended for them.
Okay, this will need quite a lot of thinking, which is certainly not evident at the moment. Junctions should be a top priority for cycling infrastructure because I think that it's the perceived and real hazards at junctions that put a lot of people off cycling, and create a genuine barrier. It doesn't matter how good the infrastructure is on a section of road without junctions, if you reach a junction with no infrastructure you are stuffed.
As for the Lothian Road / Princes Street junction, it is currently very intimidating no matter which 'legal' route you want to take, and there are no inherent reasons that all the 'illegal' routes shouldn't be provided for bikes. It needs a properly designed Dutch standard infrastructure that allows bikes safely to negotiate, Lothian Road, to Shandwick Place, Queensferry Street, Hope Street, Princes Street, and all the other combinations of those streets. That way we might be on track to get some good east west, and north south routes. It could be done with some imagination.