The basis of my thought was the fact that the operation of a neural network depends on very precise weights. And there are physical limits (things like uncertainty principle) to the precision by which we can measure something. So supposed we discover some technique by which we can, for a given human brain, recreate all the neurons and their interconnections completely, we will never be able to measure the weights associated with the links between the neurons with absolute precision.
I think this will result in a brain that not much better than an untrained brain of a child. So you will still have to pass this new brain through a series of training to reach it's full potential.
The same thing will happen in the case of AI. If we create a perfect AI, it won't be able to make perfect copies of itself. But only untrained versions of it. I think life may be already at the limits regarding the rate at which intelligence can be advanced.