I have worked in the healtcare industry myself for about 8 years in the past (i'm currently not working in the healthcare industry anymore), i do think you're touching a very delicate subject.
In the past, there were some really tough laws in place to protect patients data, and recently the laws seems to have gotten a lot tougher.

I remember having to encrypt all data that was being sent to the governement, upload it to a sftp whose keys were exchanged in person, then send the encryption key on a dvd via snail mail, and the password to unlock the key via text message, and the hash of the encrypted data in a signed letter to a different instance... I just wanted to point out that even in the past, the security measures with patient data were rather paranoid

The problem is that a blockchain is a public, immutable, trustless, decentralised ledger. Anything data you include in a block is there to stay.

• What if the patient changes his mind? There is no way to "erase" his data
• What if data that is considered harmless at this point in time, becomes something of great intrest/value to for example insurance companies (for example, at this moment in time, you think it might be a good idear to record your pollen alergy into a blockchain, but in 50 years pollen alergies get linked to a specific type of terminal iless and an isurance company decides to double the premiums for everybody having a pollen alergy based on this data
• I've also heared some companies saying that anonimising the patient's data is the sollution, but what if the key gets leaked? What if one of the hospital's databases gets breached and a hacker is able to link each anonymous key to a real life person?

I'm not saying it's a bad idear, i just think a person who wants to develop such a blockchain should do their homework and think about as many attack vectors as humanly possible before writing a single line of code.