When I was using Windows I had a software firewall that would ask me about every app that is trying to access the Internet and let me choose if I want to block or allow it - I would only allow the web browser, the messenger and the SSH client and completely block everything else (DroidWall and XPrivacy let you do this on Android, LittleSnitch does this on Mac, I miss such a tool on destkop GNU/Linux a huge lot).
Websockets were created sedcifically to get clients to transfer data to the server at the request of the server and without the user specifically wanting to send it.
Websockets don't inherently allow anything that isn't possible with other technologies. What they do is make certain data transfer patterns more efficient by removing the need for polling, or for redundant HTTP requests.