Your point that phone numbers and mailing addresses work in much the same way is true - but I don't think these have ever been quite as directly tied to identity as email is on the web.

Traditionally, for anything that's even slightly important, either your physical presence ultimately acted as your identity, or significant legal liability protected the non-physical identity (that is, if a court sends an important letter to you at some address, someone else who moved in to that address faces significant legal penalties if they open that letter).