I use anonymity because it implies freedom of speech. Many internet sites and browsers filter what you see. Google is a great example, if you and I google the same exact thing, our answers are completely different. Google now has a new EULA and it is not hiding the fact that it uses censorship. Facebook is another one, one I no longer use because since it's IPO it has been so obviously propped up by the US Government as a data mining and control tool. I do not always go anonymous. Steemit, for example, has a horrible privacy policy but I like the platform so I subscribe. I think that visibility is slightly less important that anonymity because you are letting yourself be used as a product when you are visible. Google, Twitter, Facistbook, or any other "Free" service is not free: You are the product, you are the livestock! FSF and other people fighting for free speech do give things away, but they do not ask you your name, what you like, or insert control mechanisms. Take your Gmail. Notice how it takes a few seconds to load? That is not because it is "slow" it was deliberately programmed in to build suspense. Some people might not see how sinister that is, but to me there's nothing nice about controlling other people. Nothing good comes of it.
RE: Being invisible on the internet