It's true that I can't register in the .edu/.mil/.gov domains. But plenty of organizations which CAN register in those domains choose to register in .com/.org/.net as well.
There's no connection, however, between registering domains and connecting to the net, and I can't see that there ever will be. My connectivity is provided by EasyStreet Online Services and my domain is registered by BulkRegister, two companies who have absolutely no reason ever to talk to one another. A zillion domains out there have been registered by domain name speculators whose domains have no meaningful net presence, and I can have a net presence without even registering a domain (though I would not do so myself).
-- George Mitchell