It's the same with other medical imaging procedures. They have machines literally costing millions but they can't afford to have a secure system for keeping and exchanging medical data.

Up until a few years ago (according to my knowledge, perhaps this is still happening) paramedics routinely used WhatsApp for sending information to A&E while en route because there simply is no proper system in place to do so.

The data would still be stored with the practitioner where it originated but it could be shared with third parties (i.e. other practitioners) if the patient consents.

I really don't see how using the patient as messenger for medical data on paper could be seen as a privacy feature. Quite to the contrary, actually: Paper documents are easily misplaced or lost and then suddenly someone has access to your medical data.