Websockets are often used for quality of life features like notifications and websites that are dynamic without needing to be refreshed. Almost went website with any kind of chat will use WS for example. Turning it off will make web browsing a little more annoying.

However websockets are also sometimes used for anti-fraud related software that can also leak information you may deem private. Disabling websockets might prevent that data from getting out but of course all this depends on your threat model.

No, it is unnecessary, and it would break many auto updating websites, for example, if you use mail in web, then your mail provider has web sockets to get notifications from server to fetch you mail.

I generally would recommend to disable javascript , and have a whitelist for websites you trust (easily achievable by ublock, or no script). If they do not have js, most attack vectors are neutralised. If you can trust a website to run js, you can trust it to run web sockets.

You say that you want to do this for "privacy" and "security" reasons. Those two are not the same. What is the exact use-case which you want to prevent?

Disabling WebSockets will cause some Websites not to work properly anymore. Especially such which rely on live updates without reloading the site (most common use-case for WebSockets).