Facebook buying Oculus was a two-billion dollar bet on virtual reality being the next big platform, and to have that bet pay off, Facebook has to play the long game, and let Oculus and the virtual reality market grow.
Facebook isn't stupid or myopic enough to require a Facebook login to use Oculus products. It makes absolutely no sense when you consider the reasons that Facebook bought Oculus.
Many details might have been different in this alternate history: price, timeline, quality, bundled games, future games as funded by Oculus, and more.
Unfortunately I don't know if any of us really have the information necessary to make a truly correct comparison.
My excitement for and willingness to spend money on the Rift was greatly decreased by the Facebook acquisition. It is of course still quite possible that the Facebook acquisition was a good move that will benefit everyone.