This is the real problem. And this ship has already sailed - google and data brokers are already creepily tracking your every online and offline move and tying them together.
Your financial providers are covered by a much, much more restrictive set of regulations preventing them from screwing you over like that.
Open Banking seems generally aimed at attacking the nasty behaviour banks have been getting away with, where they gatekeep your financial data in order to prevent you from getting any useful utility out of it unless you pay them extortionate fees.
I think life insurance is already pretty grabby with data, behind the scenes. We had a ton of data on some high value life policies we’d bought - down to records of all doctors visits. And even for lower value policies they can currently just ask you the important actuarial questions (e.g. are you a poor obese guy who smokes, rides a motorcycle & lives alone) and then deny the payout if you lied.
Given how disgustingly evil the US health insurance system is, my hope is that NZ resists the temptation to go there. I don’t have health insurance since moving back to NZ and it’s been fine. All the things I was told by the doctor “go private or the wait will be too long” turned out to have reasonable waits after all.