If you're using sockets you still need to come up with some kind of protocol on top of those sockets for the data that's being transferred - message delimiter, a data format etc. Then you have to build client libraries for that protocol.
WebSockets solve a bunch of those low level problems for you, in a well specified way with plenty of existing libraries.
Sure, in principle. Someone already mentioned binary data, then you come up with a framing scheme and get to write protocol documentation, but why? What's the benefit?
Now solve for encryption, authorization, authentication...
WS(S) has in the box solutions for a lot of these... on top of that, application gateways, distribution, failover etc. You get a lot of already solved solutions in the box, so to speak. If you use raw sockets, now you have to implement all of these things yourself, and you aren't gaining much over just using WSS.
Even beyond that: the ASCII delimiter control codes are perfectly valid UTF-8 (despite not being printable), so using them for in-band signaling is a recipe for pain on arbitrary UTF-8 data.
If you know your data is UTF-8, then bytes 0xFE and 0xFF are guaranteed to be free. Strictly speaking, 0xC0, 0xC1, and 0xF5 through 0xFD also are, but the two top values are free even if you are very lax and allow overlong encodings as well as codepoints up to 2³² − 1.
WebSockets solve a bunch of those low level problems for you, in a well specified way with plenty of existing libraries.