In general, if publishers are automatically sharing to Facebook without some kind of delay, people will just stay on Facebook. Also consider the private groups on Facebook, they could be sharing paid subscriptions and who would know?
The idea isn't just about Facebook, but publishing anything to get more subscribers. If your posts are time-sensitive and people can get your info through social media (without delay) then you're probably losing traffic, because people are busy, lazy, whatever--they're often already on Facebook and need a reason to go somewhere else.
Paid subscriptions aren't as common, and I almost deleted that part of my comment, but people do pay for time-sensitive info. As far as the "paid tier" I was thinking out loud, in terms of building a general purpose SAS app for publishers. I haven't nailed down exactly how it would work, to delay posts to social media. Obviously it would need compelling case studies where people increased traffic and subscribers, and revenue. I can think of a couple of markets to start with, but not getting more specific than that.
Another aspect of this is the notifications. I think email notifications are good to start with because they show up on your phone, and if those notifications are customizable and targeted, that's convenient. But I think there's more you could do with notifications, so that people aren't annoyed that they have to go to your website to find the (timely) information they want. If you can do better notifications than social media (more specific, less annoying) then I think people will more likely go to your website vs. consume your content through social media which sends less-useful notifications.