A common phenomenon in API design is to expose something simply because you've already put in all the effort required to implement it. For example, if your language runtime implements unbounded recursion, you've already gone a long way towards representing continuations as data. In that case, it's not much more work to offer first-class continuations as a data structure in the language. Similarly, languages often optimize their startup time by dumping the heap into a persistent data structure so they can cache the initialization of the standard library; once they've done this, heap-dumping is an easy feature to offer to users.
On a semantic level, first-class continuations and first-class stores are obviously similar kinds of constructs. But I'd never noticed till now how they can both just sort of crop up as natural consequences of incidental needs in language implementations.