I think that a powerful argument when people come to talking about banning people from cycling in any one location is to highlight that travelling from east to west here there are no safe and sensible options.
If anyone hasn't got out a map to look at this it's worth doing. You think that there are safe options, but take a look. There are no half-reasonable routes at all. Even the NCN route, with its own practical kerb-hopping failings and grumpy pedestrians, involves crossing often in front of parked coaches. My other half was almost knocked down there travelling west by a coach on the same day that Zhi Min Soh died. And exiting from the extreme cobbles of Randolph Place can be nasty - I've had an incident there with someone turning right across my path from Melville St.
If you go looking for an east-west route by travelling south down Lothian road you're faced with nasty right turns. And you're pretty much committed as far south as the canal or the tangle to get onto Morrison St. If you travel north looking for a route you're pretty much set to end up in Stockbridge.
About the only doable thing is to use Hope Street - which means really major and silly north-south zig-zags - and it's far from being a safe and lovely route itself.
So 'which safe route would you like me to use instead' seems like quite a powerful question. "Actually now you come to mention it I just want to ban cycling everywhere" is easier to argue against than "I'm just looking out for your welfare"...