I very much doubt that this will make life any safer for pedestrians or cyclists. Edinburgh is already a very cycle-friendly city apart from the huge numbers of potholes.
Can I suggest to the council leaders that before they introduce their widespread 20mph limit that they organise a trial day when all vehicles are asked to drive within the new limit.
I would suggest Wednesday, 1 April for the trial. This will give everyone a chance to experience what the new speed limit will be like.
If it is as bad as I expect it will be, then perhaps they could revisit the decision and only introduce the new limit in residential areas and around schools and parks.
It is quite difficult to drive at 20mph or less. I presume anyone caught doing 30mph in a 20 limit would be liable to lose their licence and face a substantial fine given they would be driving at one and a half times over the speed limit. I did my own mini-trial in my VW Golf and had to drive in second gear to keep the car below 20mph.