One thing a peer-to-peer architecture for Open Access distribution could enable would be the ability to put a whole bunch of experiment data and supporting documentation online for cheap/free as part of the journal article. Part of the reason it's difficult to replicate some scientific results is lack of access to the data and poor documentation. A series of photos and video of the experiment, access to the full experimental data set was never practical for traditional journals, is expensive to do with traditional Open Access as the researchers would have to pay the hosting fees (indirectly as part of the publication fee), but would be trivial with a peer-to-peer distribution model for the data. It'd also allow a really easy and cheap way for enthusiasts to contribute to science by acting as seeds for non-profit open access journals.
From personal experience, I produce tens of gigabytes of supporting data, photos, and video for each experiment that never gets published, in part because justifying the hosting fee is difficult. Peer-to-peer distribution of this data as part of an open access journal article would make it a lot easier.