The first wave of accounts is up for renewal on April 14 — just seven weeks from now. So App.net has seven weeks to convince its early adopters that it’s worth paying more money for another year of service.
I'm pretty sure this is incorrect. Those of us that signed up for the $50/year deal got our subscriptions extended when the price dropped to $36. My renewal date is April 9th 2014 (i.e. more than a year away).
Setting aside that piece of nit picking, Marco's completely right that in order for App.net to be useful to both end users and developers it first needs to be popular. It's a chicken and egg problem in some ways (no users without interesting apps, no interesting apps without a lot of users). Opening the doors with invite-only free accounts goes some of the way towards solving that problem without the scaling issues that would come with unrestricted free accounts.