I would guess the elephant in the room would be data security. If you, in that sense, own something you would have the right to chose who and if your data gets collected and redistributed. You might even want to participate in such events for a price (basically sell your data). The problem with that is how can we really be sure that our data is not being used? I guess you could implement outside agencies to monitor the platform. And paying rent for a property on that network would not automatically constitute having the right to one's intellectual property (and I would argue you can view personal data as intellectual property)