The thing about all this check-in deals is that it solves mostly the first problem - customer acquisition. Loyalty deals are great for customer retention, but for that part of the puzzle, I'm wondering why businesses would, and seem to want to, rely on an intermediary to manage the relationships. Allowing Facebook or any other site to be a key part in managing loyalty seems like one step away of losing all customers (or at least the data of them).
Costs and reach. The costs for a single business to implement something like this would be, I imagine, prohibitive. Their is also the issue of reach. Facebook presents a platform that business can build on that people really use. Facebook has users. A lot of users.
To implement the same system for a business, they'd have to deploy their own hardware and software, and then reach out to customers to use their special set up. Sitting on top of Facebook essentially gives them all of this without a problem. Most places can't do what Facebook is providing for them.
So now users have a reason to "Place" themselves at a business, and businesses have a reason to link into the system. A "Place" by a user gives them exposure to the users friends.
Consider also that this isn't the only means a business can use for loyalty. Business still have other means to go for customer retention.
To be fair, they can get a not insignificant part of the benefit by putting a sign outside the venue saying "checkin on Facebook for X" and asking at the counter.
They can then using that list compiled and stored for them for free by Facebook to generate a free mailing list which they can send free messages to and get free metrics on their success.
Most of the most effective ways of marketing on Facebook are free.
