It's not easy to scale deep learning because deep neural nets have a very strong tendency to overfit to their training dataset and are very bad at generalising outside their training dataset.
In a medical context this means that, while a particular deep learning image classifier might be very good at recognising cancer in images of patients' scans collected from a specific hospital, the same classifier will be much worse in the same task on images from a different hospital (or even from a different department in the same hospital).
To overcome this limitation, the only thing anyone knows that works to some extent is to train deep neural nets with a lot of data. If you can't avoid overfitting, at least you can try to overfit to a big enough sample that most common kinds of instances in your domain of interest will be included in it.
So basically to scale a diagnostic system based on deep neural net image classification to the nation level one would have to train a deep learning image classifier with the data from all hospitals in that nation.
This is not an easy task, to say the least. It's not undoable, but it's not as simple as having someone at Hospital X download a pretrained model in Tensorflow and train its last few layers on some CT scans.