FHIR will take over, but I wouldn't call that a good thing. the development of FHIR is extremely haphazard, most of it will turn into a generic KV store and miss a lot of the great systems thinking in EDI. It's as if they lowered the barrier to entry at the expense of robust document exchange.

Hopefully Stedi can make adopting EDI easier and increase its popularily over the next 50 years and there isn't such a demand to create alternative systems.