Sorry, that was hastily written and poorly worded -- more accurately, we would AT LEAST, need browsers that support TCP connections in order to connect to the p2p networks that we already have. In practice we would need a lot more, as even apps like BitTorrent and blockchains still rely on our centralized internet infrastructure to some degree.
You mention the BitTorrent DHT, but I don't believe that it's necessary to connect to a centralized super-node. You do, however; need the address of at least one other peer to start. Unfortunately, the only way to assign an address is through our ISP system which is centralized. For true peer-to-peer architecture, normal people would have to connect the internet at the same level that ISPs such as Comcast and AT&T connect to each other... think some sort of large scale mesh network.