Wouldn't a blockchain make you vulnerable to a 51% attack? Imagine someone now has access to most people's health data - I'd imagine that's worth billions even on the black market.
You're assuming a mining based system. I don't think it would be a good idea to run this on Ethereum (for instance) at all.
I am admittedly not an expert on blockchain. So without mining, what makes this different from just having a voting mechanism where you need a majority?