It's easier to communicate via TCP sockets when you're working within an intranet boundary, since you likely have control over the machines on that network and can open ports suitable for making the TCP connections.
Over the internet, you're communicating with someone else's server on the other end. They are extremely unlikely to have any old socket open for connections. Usually they will have only a few standard ones such as port 80 for HTTP or 443 for HTTPS. So, to communicate with the server you are obliged to connect using one of those ports.
Given that these are standard ports for web servers that generally speak HTTP, you're therefore obliged to conform to the HTTP protocol, otherwise the server won't talk to you. The purpose of web sockets is to allow you to initiate a connection via HTTP, but then negotiate to use the web sockets protocol (assuming the server is capable of doing so) to allow a more "TCP socket"-like communication stream.
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