I'm no expert on blockchain tech by any means, but I'd love to hear good ideas about how it could be implemented anywhere in the healthcare field, pharmacy services in particular, and if it would truly offer an advantage.
The one place that is has occurred to me (note: occurred - I've not put any serious thought in to this) would be in the distribution of controlled drugs. Where I work, controlled drugs (opiates, ketamine, benzodiazepines, etc) come from manufacturer to the hospital pharmacy, and then from there are distributed to the main ward or theatre reception, and then from there are split as required to individual wards or theatres and locked in secure cupboards. At each stage of this process there is a manual count of stock between the deliverer and receiver, and both sign off that the numbers are correct. When a drug is to be used, again two members of staff must count the stock in the cupboard and sign off that records are correct. When stock is low, an order from the ward or theatre is placed with their main reception, which collaborates these orders and puts in a bigger order to hospital pharmacy, which then does the same with the manufacturer.
A distributed database could maybe help this in two ways - firstly by streamlining the whole "two member of staff signing off ", which is generally done on paper and then centrally collated, and secondly by displaying levels of stock in real time available for all to see to automate the ordering process. I suspect the reason that I have never seen this suggested before is that all these people shilling their "healthcare ICO/blockchain project" have never actually worked in healthcare, and have no idea of the real world challenges or issues.