I've read recent papers about verifiable delay functions (Boneh et al 2018) and proof of sequential works (Cohen et al. 2018). I understand that the core difference between the definitions is that a VDF output is required to be unique (while in PoSW constructions - many commitments can prove knowledge of the same x w.h.p.).
But... why does it matter? Namely, what are the applications that use VDF, and that rely heavily on this uniqueness property such that replacing the VDF with the PoSW won't suffice?
For example, the Randomness Beacon - one of the basic motivations for VDF, can use PoSW as well, no?