Is there any way to use raw socket on web support in Flutter?

I'm using tcp socket server with c++, and the Server makes connection through raw socket with mobile application(in Flutter).

Now, I want to use Web platform in Flutter, but I can't use the socket I had used(not supported on web platform).

Instead, there are some of web socket or http packages.

I'm not familiar with the web, so I don't know the reason why raw tcp socket is not used commonly on web platform.
The reason I want to use raw socket is that, I feel like that http or websocket might be slower than raw socket. Data size transferred between server and client(mobile application now) is about 4mb per second in maximum.

Is there any way to use raw socket on web support of Flutter?

Or, Do I have to add websocket server as a proxy server on c++ server..?

Oor, any other better way?

Thanks in advance.