This is for services that don't need to email users but want to remember them across devices. You're lowering the barrier to entry somewhat but you still have a barrier just to provide the cross-device feature. Why not remove the barrier completely by just using cookies, and then later after the user has created enough state, and is presumably hooked to your service, give them the option to add the cross-device feature. You might even have enough goodwill at that point to be able to ask them for their email without having to use Facebook as a crutch.
I think <guelo>'s advice above is sound. I learned this lesson myself after testing early versions of http://recent.io -- there's a high barrier to convincing users to type in an email address and password, even if it's for personalized news recommendations across multiple devices. It's not necessarily a trust issue -- it's simply a hurdle. Fortunately there are other ways to do it...
