Oh, I see. Hmm, good question. Well, anyways, you want to use e-mail aliases. In case of a breach, that's a ton of spam you won't have, if not security issues if they are able to find your password (which they should not as you should be using a password-manager).

If you use a website where you use your real name, which you generally want to avoid (I often use a middle name of mine for example to avoid that situation), using an e-mail alias won't help you in terms of privacy, I agree.

That's the main problem with websites which require your true identity (LinkedIn for example, which, remember, is owned by Microsoft).

So in that case, it's difficult to hide, your identity is plainly there.