I think it's already taking off and the key difference between now and then is virtualisation. This provides a stable target and avoids the pain of having to deal with device drivers while also providing good isolation.
Another way of looking at it is that the libOS's time has come. Early versions like Exokernel and Nemesis were ahead of their time but the wider ecosystem is now ready to make use of new implementations. Also, Unikernel is a more general term, whereas Exokernel was largely for a specific project.
You might find the following two references useful.