I've seen the "cheapium" model used for mobile apps, and am currently using on a B2C app that launched last week, and have a client considering it for a B2B app in the future.
We've had a little pushback that "You can't charge me for the App and then charge me again for an upgrade to unlimited items" - but otherwise it's going well so far.
Clearly, putting a starting price, no matter how low, on an app is a barrier to entry. There are many people who simply will not pay for an app. You have to decide whether your product needs wide exposure or (potentially) higher quality customers.
Freemium, Cheapium or Full paid - there is no right answer, and you can spend weeks discussing it and still not come to a satisfactory conclusion.