Suppose early on in my life I incurr $1,999,999 in expenses. Then, later on I have an unexpected accident that costs $2. Prima facie the system should still fund this. However, your system, by not focusing on the margins, does not satisfy this.

Also, you probably want a smoother tail. Your system would spend $2m to extend the life of a 74 year old by a year, but nothing to extend the life of a 75 year old by 20 years.

Also, I don't think that, in equilibrium, health insurance companies are actually incentivised to fund research into longevity. This would only make policies cheaper if consumers hadn't already taken into account the increases to lifespan.

Finally, I think this post would be improved if you hadn't mentioned its making public healthcare easier - Politics is the Mind-Killer.