Only if we are talking about the custody of a purely digital asset, or purely digital information (as in not linked to anything in the real/physical world).
> For example, imagine how blockchain could solve the problem of a patient who has control of their health records....
If you have control over your own "blockchain" medical records, what is stopping you from omitting the last few records too? How is this going to stop your data from being leaked by someone who hacks your current doctor? How will all doctors be forced to use it (if it is not put into law by a government body) and this case, why would this be chosen vs a centralised system? Who will be "mining" and why?
What happens if you are taken to an ER, and you are not conscious? How will the ER get your records if they are somehow sealed? All it takes would be some dying because of lack of access to the records for the system to be scrapped. As people would be more interested in saving lives vs worrying about governments and corporations snooping on them. Hell today we are giving up our privacy for things are mundane and pointless like Social Media.