Why do you need to sign up for Facebook? Can't everything be done in the browser?
Other than getting BCH, what's out of browser?
Sign up implies making an account with a trusted server. You don't *need* to sign up on memo.cash, you can just use your private key on any OP_return compatible wallet to make memos.
memo.cash isn't the only way to read/write memo data. There are a few other clients, but the only wallet I'm aware of is the Telescope wallet, which is a browser extension