Besides breaking a lot of language invariants, first-class continuations would be a nightmare for portability, since different implementations implement different API's natively. Either you mandate capturing continuations across native frames, which is a hardship for implementers and a performance-killer, or you don't, which causes observably different behavior across browsers when they place native delimiters at different points in the continuations-- leading to lots of painful bug reports and nasty market dynamics where everyone has to tailor their implementations to track the most popular.
So that won't happen. But!
What we're talking about here is a restricted version of delimited continuations: the delimiters are implicit--they're at function boundaries. But otherwise it's very much in that space. And there's a loooot of prior work on this topic. I'll post later with a little background and some notes about the design space of delimited continuations for ES.