Are you a small time supplier, and want a major retailer to integrate with you over API? good luck. The decision really isn't yours, if you want to get paid, you integrate.
I think the reality is that most developers would rather use an JSON API instead of EDI. EDI is sometimes talked about as just X12 / EDIFACT, but the protocol is baked in as well, which causes more headache (who wants to build an EDI stack?). X12 was built during a time where VANs probably connectivity, and caused per character, so everything was positional based and inferred. Modern APIs are descriptive, and easier to use.
(fd: I work for Orderful, a company that provides an API and then translates it to EDI so you can easily work with any trading partner)