Neither the PlayStation 4 nor the Xbox One allows players to stream Bioshock: The Collection, and despite 2K acknowledging this they haven't given a reason as to why this is the case.
2K have said that "unfortunately, streaming BioShock: The Collection isn't an option right now. We will update this article should this situation change." Who knows what will happen in the future, but we know for sure there's no streaming of Rapture or Columbia right now.
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